Statistical calculator 2007

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Statistical calculator 2007 Powered By Docstoc
					Statistical Calculator
Table of Contents

          Normal distribution and probability (area to the left)
          Normal distribution and probability (area to the right)
          Normal distribution and probability (area between two values)
          Descriptive statistics and outliers
          Histogram
          Box plot (up to five box plots on the same graph)
          Box plot (with outliers)
          Stem and leaf plot (leaf unit >1)
          Stem and leaf plot (leaf unit =1)
          Split stem and leaf plot
          Back-to-back stem and leaf plot

          Note: The sample size up to 1000 observations is allowed. The worksheets are protected.
                However, you may remove the protection (password is not required) if you want to check
                the formula behind the calculation.

This version: 17 September 2012
                   Normal quantile plot
                   Regression
                   Random variable
                   Binomial distribution
                   Inference for one proportion
                   Inference for two proportions
                   Inference about one population mean
                   Inference about two population means
                   Inference in the matched pairs design
                   Two-way tables and chi-square tests
                   Two-way table (enter the raw data here)

wed. The worksheets are protected.
word is not required) if you want to check
Draw a normal distribution and calculate probabilities                                       Back to Content
Area to the left

Mean                               15           There is a 25.25% chance that a score selected at random would
Sigma                               3           be 13 or less, or that 25.25% of all the scores will be 13 or less.
X1                                 13
Z1                       -0.666666667
Operator1         <=
P(X <= 13)               0.252492538
X2
Z2
Operator2
Probability

Insert the title for the diagram here:




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                                                                      11

                                                                      14

                                                                      17
                                                                      19
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                                                                      22
                                                                       5




                                                                      13

                                                                      16




                                                                      24
      Mean = 15, sigma = 3


                                        Mean = 15, sigma = 3
            0.14000


            0.12000


            0.10000


            0.08000
     f(X)




                                                                                                   Remaining area

            0.06000                                                                                Area for <= 13



            0.04000


            0.02000


            0.00000
                       5
                       5
                       6
                       7
                       8
                       9
                      10




                      14
                      15
                      16
                      17
                      18
                      19
                      20
                      21




                      25
                      11
                      12
                      13
                      13




                      22
                      22
                      23
                      24




      x               Remaining area     z      Area for <= 13
    4.50                 0.00029        -3.50       0.000290894
    4.53                 0.00030        -3.49       0.000301241
    4.56                 0.00031        -3.48       0.000311924
    4.59                 0.00032        -3.47       0.000322954
    4.62                 0.00033        -3.46        0.00033434
    4.65                 0.00035        -3.45       0.000346094
    4.68                 0.00036        -3.44       0.000358224
    4.71                 0.00037        -3.43       0.000370743
    4.74                 0.00038        -3.42       0.000383661
    4.77                 0.00040        -3.41       0.000396989
4.80   0.00041   -3.40    0.00041074
4.83   0.00042   -3.39   0.000424924
4.86   0.00044   -3.38   0.000439554
4.89   0.00045   -3.37   0.000454642
4.92   0.00047   -3.36   0.000470201
4.95   0.00049   -3.35   0.000486244
4.98   0.00050   -3.34   0.000502784
5.01   0.00052   -3.33   0.000519834
5.04   0.00054   -3.32   0.000537409
5.07   0.00056   -3.31   0.000555523
5.10   0.00057   -3.30    0.00057419
5.13   0.00059   -3.29   0.000593424
5.16   0.00061   -3.28   0.000613242
5.19   0.00063   -3.27   0.000633658
5.22   0.00065   -3.26   0.000654689
5.25   0.00068   -3.25   0.000676349
5.28   0.00070   -3.24   0.000698657
5.31   0.00072   -3.23   0.000721628
5.34   0.00075   -3.22    0.00074528
5.37   0.00077   -3.21    0.00076963
5.40   0.00079   -3.20   0.000794696
5.43   0.00082   -3.19   0.000820497
5.46   0.00085   -3.18    0.00084705
5.49   0.00087   -3.17   0.000874375
5.52   0.00090   -3.16   0.000902492
5.55   0.00093   -3.15   0.000931419
5.58   0.00096   -3.14   0.000961178
5.61   0.00099   -3.13   0.000991788
5.64   0.00102   -3.12   0.001023271
5.67   0.00106   -3.11   0.001055648
5.70   0.00109   -3.10    0.00108894
5.73   0.00112   -3.09   0.001123169
5.76   0.00116   -3.08   0.001158359
5.79   0.00119   -3.07   0.001194532
5.82   0.00123   -3.06   0.001231711
5.85   0.00127   -3.05   0.001269921
5.88   0.00131   -3.04   0.001309185
5.91   0.00135   -3.03   0.001349527
5.94   0.00139   -3.02   0.001390974
5.97   0.00143   -3.01   0.001433551
6.00   0.00148   -3.00   0.001477283
6.03   0.00152   -2.99   0.001522197
6.06   0.00157   -2.98   0.001568319
6.09   0.00162   -2.97   0.001615678
6.12   0.00166   -2.96     0.0016643
6.15   0.00171   -2.95   0.001714214
6.18   0.00177   -2.94   0.001765448
6.21   0.00182   -2.93   0.001818032
6.24   0.00187   -2.92   0.001871995
6.27   0.00193   -2.91   0.001927366
6.30   0.00198   -2.90   0.001984177
6.33   0.00204   -2.89   0.002042459
6.36   0.00210   -2.88   0.002102242
6.39   0.00216   -2.87   0.002163559
6.42   0.00223   -2.86   0.002226441
6.45   0.00229   -2.85   0.002290922
6.48   0.00236   -2.84   0.002357035
6.51   0.00242   -2.83   0.002424813
6.54   0.00249   -2.82   0.002494291
6.57   0.00257   -2.81   0.002565503
6.60   0.00264   -2.80   0.002638484
6.63   0.00271   -2.79    0.00271327
6.66   0.00279   -2.78   0.002789896
6.69   0.00287   -2.77     0.0028684
6.72   0.00295   -2.76   0.002948818
6.75   0.00303   -2.75   0.003031188
6.78   0.00312   -2.74   0.003115546
6.81   0.00320   -2.73   0.003201932
6.84   0.00329   -2.72   0.003290385
6.87   0.00338   -2.71   0.003380942
6.90   0.00347   -2.70   0.003473645
6.93   0.00357   -2.69   0.003568533
6.96   0.00367   -2.68   0.003665646
6.99   0.00377   -2.67   0.003765025
7.02   0.00387   -2.66   0.003866712
7.05   0.00397   -2.65   0.003970748
7.08   0.00408   -2.64   0.004077175
7.11   0.00419   -2.63   0.004186037
7.14   0.00430   -2.62   0.004297375
7.17   0.00441   -2.61   0.004411234
7.20   0.00453   -2.60   0.004527656
7.23   0.00465   -2.59   0.004646687
7.26   0.00477   -2.58    0.00476837
7.29   0.00489   -2.57    0.00489275
7.32   0.00502   -2.56   0.005019872
7.35   0.00515   -2.55   0.005149782
7.38   0.00528   -2.54   0.005282526
7.41   0.00542   -2.53    0.00541815
7.44   0.00556   -2.52     0.0055567
7.47   0.00570   -2.51   0.005698223
7.50   0.00584   -2.50   0.005842767
7.53   0.00599   -2.49   0.005990378
7.56   0.00614   -2.48   0.006141104
7.59   0.00629   -2.47   0.006294992
7.62   0.00645   -2.46   0.006452092
7.65   0.00661   -2.45   0.006612451
7.68   0.00678   -2.44   0.006776119
7.71   0.00694   -2.43   0.006943142
7.74   0.00711   -2.42   0.007113572
7.77   0.00729   -2.41   0.007287456
7.80   0.00746   -2.40   0.007464843
7.83   0.00765   -2.39   0.007645785
7.86   0.00783   -2.38   0.007830328
7.89   0.00802   -2.37   0.008018525
7.92   0.00821   -2.36   0.008210423
7.95   0.00841   -2.35   0.008406073
7.98   0.00861   -2.34   0.008605525
8.01   0.00881   -2.33   0.008808828
8.04   0.00902   -2.32   0.009016033
8.07   0.00923   -2.31   0.009227189
8.10   0.00944   -2.30   0.009442346
8.13   0.00966   -2.29   0.009661554
8.16   0.00988   -2.28   0.009884862
8.19   0.01011   -2.27    0.01011232
8.22   0.01034   -2.26   0.010343977
8.25   0.01058   -2.25   0.010579884
8.28   0.01082   -2.24   0.010820089
8.31   0.01106   -2.23    0.01106464
8.34   0.01131   -2.22   0.011313588
8.37   0.01157   -2.21    0.01156698
8.40   0.01182   -2.20   0.011824864
8.43   0.01209   -2.19    0.01208729
8.46   0.01235   -2.18   0.012354303
8.49   0.01263   -2.17   0.012625953
8.52   0.01290   -2.16   0.012902285
8.55   0.01318   -2.15   0.013183347
8.58   0.01347   -2.14   0.013469185
8.61   0.01376   -2.13   0.013759843
8.64   0.01406   -2.12   0.014055369
8.67   0.01436   -2.11   0.014355806
8.70   0.01466   -2.10   0.014661199
8.73   0.01497   -2.09   0.014971591
8.76   0.01529   -2.08   0.015287025
8.79   0.01561   -2.07   0.015607545
8.82   0.01593   -2.06   0.015933192
8.85   0.01626   -2.05   0.016264006
8.88   0.01660   -2.04   0.016600029
8.91   0.01694   -2.03     0.0169413
8.94   0.01729   -2.02   0.017287859
8.97   0.01764   -2.01   0.017639743
9.00   0.01800   -2.00   0.017996989
9.03   0.01836   -1.99   0.018359634
9.06   0.01873   -1.98   0.018727714
9.09   0.01910   -1.97   0.019101263
9.12   0.01948   -1.96   0.019480315
9.15   0.01986   -1.95   0.019864902
9.18   0.02026   -1.94   0.020255056
9.21   0.02065   -1.93   0.020650808
9.24   0.02105   -1.92   0.021052187
9.27   0.02146   -1.91   0.021459221
9.30   0.02187   -1.90   0.021871938
9.33   0.02229   -1.89   0.022290364
9.36   0.02271   -1.88   0.022714522
9.39   0.02314   -1.87   0.023144437
9.42   0.02358   -1.86   0.023580131
9.45   0.02402   -1.85   0.024021625
9.48   0.02447   -1.84   0.024468938
9.51   0.02492   -1.83   0.024922087
9.54   0.02538   -1.82   0.025381091
9.57   0.02585   -1.81   0.025845964
9.60   0.02632   -1.80   0.026316719
9.63   0.02679   -1.79    0.02679337
9.66   0.02728   -1.78   0.027275925
9.69   0.02776   -1.77   0.027764395
9.72   0.02826   -1.76   0.028258787
9.75   0.02876   -1.75   0.028759106
9.78   0.02927   -1.74   0.029265357
9.81   0.02978   -1.73   0.029777541
9.84    0.03030   -1.72    0.03029566
9.87    0.03082   -1.71   0.030819711
9.90    0.03135   -1.70   0.031349692
9.93    0.03189   -1.69   0.031885599
9.96    0.03243   -1.68   0.032427423
9.99    0.03298   -1.67   0.032975157
10.02   0.03353   -1.66   0.033528789
10.05   0.03409   -1.65   0.034088308
10.08   0.03465   -1.64   0.034653698
10.11   0.03522   -1.63   0.035224944
10.14   0.03580   -1.62   0.035802025
10.17   0.03638   -1.61   0.036384922
10.20   0.03697   -1.60   0.036973612
10.23   0.03757   -1.59   0.037568069
10.26   0.03817   -1.58   0.038168267
10.29   0.03877   -1.57   0.038774176
10.32   0.03939   -1.56   0.039385765
10.35   0.04000   -1.55      0.040003
10.38   0.04063   -1.54   0.040625846
10.41   0.04125   -1.53   0.041254263
10.44   0.04189   -1.52   0.041888212
10.47   0.04253   -1.51    0.04252765
10.50   0.04317   -1.50   0.043172532
10.53   0.04382   -1.49    0.04382281
10.56   0.04448   -1.48   0.044478435
10.59   0.04514   -1.47   0.045139354
10.62   0.04581   -1.46   0.045805513
10.65   0.04648   -1.45   0.046476855
10.68   0.04715   -1.44   0.047153322
10.71   0.04783   -1.43    0.04783485
10.74   0.04852   -1.42   0.048521377
10.77   0.04921   -1.41   0.049212835
10.80   0.04991   -1.40   0.049909155
10.83   0.05061   -1.39   0.050610267
10.86   0.05132   -1.38   0.051316096
10.89   0.05203   -1.37   0.052026565
10.92   0.05274   -1.36   0.052741597
10.95   0.05346   -1.35   0.053461109
10.98   0.05419   -1.34   0.054185018
11.01   0.05491   -1.33   0.054913238
11.04   0.05565   -1.32   0.055645681
11.07   0.05638   -1.31   0.056382254
11.10   0.05712   -1.30   0.057122864
11.13   0.05787   -1.29   0.057867416
11.16   0.05862   -1.28    0.05861581
11.19   0.05937   -1.27   0.059367946
11.22   0.06012   -1.26   0.060123721
11.25   0.06088   -1.25   0.060883028
11.28   0.06165   -1.24    0.06164576
11.31   0.06241   -1.23   0.062411806
11.34   0.06318   -1.22   0.063181053
11.37   0.06395   -1.21   0.063953385
11.40   0.06473   -1.20   0.064728685
11.43   0.06551   -1.19   0.065506833
11.46   0.06629   -1.18   0.066287706
11.49   0.06707   -1.17   0.067071181
11.52   0.06786   -1.16   0.067857129
11.55   0.06865   -1.15   0.068645423
11.58   0.06944   -1.14    0.06943593
11.61   0.07023   -1.13   0.070228517
11.64   0.07102   -1.12   0.071023049
11.67   0.07182   -1.11   0.071819387
11.70   0.07262   -1.10   0.072617392
11.73   0.07342   -1.09   0.073416922
11.76   0.07422   -1.08   0.074217833
11.79   0.07502   -1.07   0.075019978
11.82   0.07582   -1.06   0.075823211
11.85   0.07663   -1.05    0.07662738
11.88   0.07743   -1.04   0.077432335
11.91   0.07824   -1.03   0.078237921
11.94   0.07904   -1.02   0.079043984
11.97   0.07985   -1.01   0.079850366
12.00   0.08066   -1.00   0.080656908
12.03   0.08146   -0.99    0.08146345
12.06   0.08227   -0.98    0.08226983
12.09   0.08308   -0.97   0.083075884
12.12   0.08388   -0.96   0.083881447
12.15   0.08469   -0.95   0.084686352
12.18   0.08549   -0.94   0.085490431
12.21   0.08629   -0.93   0.086293516
12.24   0.08710   -0.92   0.087095434
12.27   0.08790   -0.91   0.087896014
12.30   0.08870   -0.90   0.088695083
12.33   0.08949   -0.89   0.089492467
12.36   0.09029   -0.88   0.090287991
12.39   0.09108   -0.87   0.091081477
12.42   0.09187   -0.86   0.091872749
12.45   0.09266   -0.85   0.092661629
12.48   0.09345   -0.84   0.093447937
12.51   0.09423   -0.83   0.094231494
12.54   0.09501   -0.82   0.095012119
12.57   0.09579   -0.81   0.095789632
12.60   0.09656   -0.80   0.096563851
12.63   0.09733   -0.79   0.097334593
12.66   0.09810   -0.78   0.098101677
12.69   0.09886   -0.77   0.098864918
12.72   0.09962   -0.76   0.099624135
12.75   0.10038   -0.75   0.100379144
12.78   0.10113   -0.74   0.101129761
12.81   0.10188   -0.73   0.101875803
12.84   0.10262   -0.72   0.102617087
12.87   0.10335   -0.71   0.103353428
12.90   0.10408   -0.70   0.104084644
12.93   0.10481   -0.69   0.104810552
12.96   0.10553   -0.68   0.105530969
12.99   0.10625   -0.67   0.106245713
13.02   0.10695   -0.66
13.05   0.10766   -0.65
13.08   0.10835   -0.64
13.11   0.10904   -0.63
13.14   0.10973   -0.62
13.17   0.11040   -0.61
13.20   0.11107   -0.60
13.23   0.11174   -0.59
13.26   0.11239   -0.58
13.29   0.11304   -0.57
13.32   0.11368   -0.56
13.35   0.11431   -0.55
13.38   0.11494   -0.54
13.41   0.11556   -0.53
13.44   0.11616   -0.52
13.47   0.11676   -0.51
13.50   0.11736   -0.50
13.53   0.11794   -0.49
13.56   0.11851   -0.48
13.59   0.11908   -0.47
13.62   0.11963   -0.46
13.65   0.12018   -0.45
13.68   0.12071   -0.44
13.71   0.12124   -0.43
13.74   0.12175   -0.42
13.77   0.12226   -0.41
13.80   0.12276   -0.40
13.83   0.12324   -0.39
13.86   0.12372   -0.38
13.89   0.12418   -0.37
13.92   0.12464   -0.36
13.95   0.12508   -0.35
13.98   0.12551   -0.34
14.01   0.12593   -0.33
14.04   0.12634   -0.32
14.07   0.12674   -0.31
14.10   0.12713   -0.30
14.13   0.12750   -0.29
14.16   0.12787   -0.28
14.19   0.12822   -0.27
14.22   0.12856   -0.26
14.25   0.12889   -0.25
14.28   0.12921   -0.24
14.31   0.12951   -0.23
14.34   0.12980   -0.22
14.37   0.13008   -0.21
14.40   0.13035   -0.20
14.43   0.13060   -0.19
14.46   0.13084   -0.18
14.49   0.13107   -0.17
14.52   0.13129   -0.16
14.55   0.13149   -0.15
14.58   0.13168   -0.14
14.61   0.13186   -0.13
14.64   0.13203   -0.12
14.67   0.13218   -0.11
14.70   0.13232   -0.10
14.73   0.13244   -0.09
14.76   0.13256   -0.08
14.79   0.13266   -0.07
14.82   0.13274   -0.06
14.85   0.13281   -0.05
14.88   0.13287   -0.04
14.91   0.13292   -0.03
14.94   0.13295   -0.02
14.97   0.13297   -0.01
15.00   0.13298   0.00
15.03   0.13297   0.01
15.06   0.13295   0.02
15.09   0.13292   0.03
15.12   0.13287   0.04
15.15   0.13281   0.05
15.18   0.13274   0.06
15.21   0.13266   0.07
15.24   0.13256   0.08
15.27   0.13244   0.09
15.30   0.13232   0.10
15.33   0.13218   0.11
15.36   0.13203   0.12
15.39   0.13186   0.13
15.42   0.13168   0.14
15.45   0.13149   0.15
15.48   0.13129   0.16
15.51   0.13107   0.17
15.54   0.13084   0.18
15.57   0.13060   0.19
15.60   0.13035   0.20
15.63   0.13008   0.21
15.66   0.12980   0.22
15.69   0.12951   0.23
15.72   0.12921   0.24
15.75   0.12889   0.25
15.78   0.12856   0.26
15.81   0.12822   0.27
15.84   0.12787   0.28
15.87   0.12750   0.29
15.90   0.12713   0.30
15.93   0.12674   0.31
15.96   0.12634   0.32
15.99   0.12593   0.33
16.02   0.12551   0.34
16.05   0.12508   0.35
16.08   0.12464   0.36
16.11   0.12418   0.37
16.14   0.12372   0.38
16.17   0.12324   0.39
16.20   0.12276   0.40
16.23   0.12226   0.41
16.26   0.12175   0.42
16.29   0.12124   0.43
16.32   0.12071   0.44
16.35   0.12018   0.45
16.38   0.11963   0.46
16.41   0.11908   0.47
16.44   0.11851   0.48
16.47   0.11794   0.49
16.50   0.11736   0.50
16.53   0.11676   0.51
16.56   0.11616   0.52
16.59   0.11556   0.53
16.62   0.11494   0.54
16.65   0.11431   0.55
16.68   0.11368   0.56
16.71   0.11304   0.57
16.74   0.11239   0.58
16.77   0.11174   0.59
16.80   0.11107   0.60
16.83   0.11040   0.61
16.86   0.10973   0.62
16.89   0.10904   0.63
16.92   0.10835   0.64
16.95   0.10766   0.65
16.98   0.10695   0.66
17.01   0.10625   0.67
17.04   0.10553   0.68
17.07   0.10481   0.69
17.10   0.10408   0.70
17.13   0.10335   0.71
17.16   0.10262   0.72
17.19   0.10188   0.73
17.22   0.10113   0.74
17.25   0.10038   0.75
17.28   0.09962   0.76
17.31   0.09886   0.77
17.34   0.09810   0.78
17.37   0.09733   0.79
17.40   0.09656   0.80
17.43   0.09579   0.81
17.46   0.09501   0.82
17.49   0.09423   0.83
17.52   0.09345   0.84
17.55   0.09266   0.85
17.58   0.09187   0.86
17.61   0.09108   0.87
17.64   0.09029   0.88
17.67   0.08949   0.89
17.70   0.08870   0.90
17.73   0.08790   0.91
17.76   0.08710   0.92
17.79   0.08629   0.93
17.82   0.08549   0.94
17.85   0.08469   0.95
17.88   0.08388   0.96
17.91   0.08308   0.97
17.94   0.08227   0.98
17.97   0.08146   0.99
18.00   0.08066   1.00
18.03   0.07985   1.01
18.06   0.07904   1.02
18.09   0.07824   1.03
18.12   0.07743   1.04
18.15   0.07663   1.05
18.18   0.07582   1.06
18.21   0.07502   1.07
18.24   0.07422   1.08
18.27   0.07342   1.09
18.30   0.07262   1.10
18.33   0.07182   1.11
18.36   0.07102   1.12
18.39   0.07023   1.13
18.42   0.06944   1.14
18.45   0.06865   1.15
18.48   0.06786   1.16
18.51   0.06707   1.17
18.54   0.06629   1.18
18.57   0.06551   1.19
18.60   0.06473   1.20
18.63   0.06395   1.21
18.66   0.06318   1.22
18.69   0.06241   1.23
18.72   0.06165   1.24
18.75   0.06088   1.25
18.78   0.06012   1.26
18.81   0.05937   1.27
18.84   0.05862   1.28
18.87   0.05787   1.29
18.90   0.05712   1.30
18.93   0.05638   1.31
18.96   0.05565   1.32
18.99   0.05491   1.33
19.02   0.05419   1.34
19.05   0.05346   1.35
19.08   0.05274   1.36
19.11   0.05203   1.37
19.14   0.05132   1.38
19.17   0.05061   1.39
19.20   0.04991   1.40
19.23   0.04921   1.41
19.26   0.04852   1.42
19.29   0.04783   1.43
19.32   0.04715   1.44
19.35   0.04648   1.45
19.38   0.04581   1.46
19.41   0.04514   1.47
19.44   0.04448   1.48
19.47   0.04382   1.49
19.50   0.04317   1.50
19.53   0.04253   1.51
19.56   0.04189   1.52
19.59   0.04125   1.53
19.62   0.04063   1.54
19.65   0.04000   1.55
19.68   0.03939   1.56
19.71   0.03877   1.57
19.74   0.03817   1.58
19.77   0.03757   1.59
19.80   0.03697   1.60
19.83   0.03638   1.61
19.86   0.03580   1.62
19.89   0.03522   1.63
19.92   0.03465   1.64
19.95   0.03409   1.65
19.98   0.03353   1.66
20.01   0.03298   1.67
20.04   0.03243   1.68
20.07   0.03189   1.69
20.10   0.03135   1.70
20.13   0.03082   1.71
20.16   0.03030   1.72
20.19   0.02978   1.73
20.22   0.02927   1.74
20.25   0.02876   1.75
20.28   0.02826   1.76
20.31   0.02776   1.77
20.34   0.02728   1.78
20.37   0.02679   1.79
20.40   0.02632   1.80
20.43   0.02585   1.81
20.46   0.02538   1.82
20.49   0.02492   1.83
20.52   0.02447   1.84
20.55   0.02402   1.85
20.58   0.02358   1.86
20.61   0.02314   1.87
20.64   0.02271   1.88
20.67   0.02229   1.89
20.70   0.02187   1.90
20.73   0.02146   1.91
20.76   0.02105   1.92
20.79   0.02065   1.93
20.82   0.02026   1.94
20.85   0.01986   1.95
20.88   0.01948   1.96
20.91   0.01910   1.97
20.94   0.01873   1.98
20.97   0.01836   1.99
21.00   0.01800   2.00
21.03   0.01764   2.01
21.06   0.01729   2.02
21.09   0.01694   2.03
21.12   0.01660   2.04
21.15   0.01626   2.05
21.18   0.01593   2.06
21.21   0.01561   2.07
21.24   0.01529   2.08
21.27   0.01497   2.09
21.30   0.01466   2.10
21.33   0.01436   2.11
21.36   0.01406   2.12
21.39   0.01376   2.13
21.42   0.01347   2.14
21.45   0.01318   2.15
21.48   0.01290   2.16
21.51   0.01263   2.17
21.54   0.01235   2.18
21.57   0.01209   2.19
21.60   0.01182   2.20
21.63   0.01157   2.21
21.66   0.01131   2.22
21.69   0.01106   2.23
21.72   0.01082   2.24
21.75   0.01058   2.25
21.78   0.01034   2.26
21.81   0.01011   2.27
21.84   0.00988   2.28
21.87   0.00966   2.29
21.90   0.00944   2.30
21.93   0.00923   2.31
21.96   0.00902   2.32
21.99   0.00881   2.33
22.02   0.00861   2.34
22.05   0.00841   2.35
22.08   0.00821   2.36
22.11   0.00802   2.37
22.14   0.00783   2.38
22.17   0.00765   2.39
22.20   0.00746   2.40
22.23   0.00729   2.41
22.26   0.00711   2.42
22.29   0.00694   2.43
22.32   0.00678   2.44
22.35   0.00661   2.45
22.38   0.00645   2.46
22.41   0.00629   2.47
22.44   0.00614   2.48
22.47   0.00599   2.49
22.50   0.00584   2.50
22.53   0.00570   2.51
22.56   0.00556   2.52
22.59   0.00542   2.53
22.62   0.00528   2.54
22.65   0.00515   2.55
22.68   0.00502   2.56
22.71   0.00489   2.57
22.74   0.00477   2.58
22.77   0.00465   2.59
22.80   0.00453   2.60
22.83   0.00441   2.61
22.86   0.00430   2.62
22.89   0.00419   2.63
22.92   0.00408   2.64
22.95   0.00397   2.65
22.98   0.00387   2.66
23.01   0.00377   2.67
23.04   0.00367   2.68
23.07   0.00357   2.69
23.10   0.00347   2.70
23.13   0.00338   2.71
23.16   0.00329   2.72
23.19   0.00320   2.73
23.22   0.00312   2.74
23.25   0.00303   2.75
23.28   0.00295   2.76
23.31   0.00287   2.77
23.34   0.00279   2.78
23.37   0.00271   2.79
23.40   0.00264   2.80
23.43   0.00257   2.81
23.46   0.00249   2.82
23.49   0.00242   2.83
23.52   0.00236   2.84
23.55   0.00229   2.85
23.58   0.00223   2.86
23.61   0.00216   2.87
23.64   0.00210   2.88
23.67   0.00204   2.89
23.70   0.00198   2.90
23.73   0.00193   2.91
23.76   0.00187   2.92
23.79   0.00182   2.93
23.82   0.00177   2.94
23.85   0.00171   2.95
23.88   0.00166   2.96
23.91   0.00162   2.97
23.94   0.00157   2.98
23.97   0.00152   2.99
24.00   0.00148   3.00
24.03   0.00143   3.01
24.06   0.00139   3.02
24.09   0.00135   3.03
24.12   0.00131   3.04
24.15   0.00127   3.05
24.18   0.00123   3.06
24.21   0.00119   3.07
24.24   0.00116   3.08
24.27   0.00112   3.09
24.30   0.00109   3.10
24.33   0.00106   3.11
24.36   0.00102   3.12
24.39   0.00099   3.13
24.42   0.00096   3.14
24.45   0.00093   3.15
24.48   0.00090   3.16
24.51   0.00087   3.17
24.54   0.00085   3.18
24.57   0.00082   3.19
24.60   0.00079   3.20
24.63   0.00077   3.21
24.66   0.00075   3.22
24.69   0.00072   3.23
24.72   0.00070   3.24
24.75   0.00068   3.25
24.78   0.00065   3.26
24.81   0.00063   3.27
24.84   0.00061   3.28
24.87   0.00059   3.29
24.90   0.00057   3.30
24.93   0.00056   3.31
24.96   0.00054   3.32
24.99   0.00052   3.33
25.02   0.00050   3.34
25.05   0.00049   3.35
25.08   0.00047   3.36
25.11   0.00045   3.37
25.14   0.00044   3.38
25.17   0.00042   3.39
25.20   0.00041   3.40
25.23   0.00040   3.41
25.26   0.00038   3.42
25.29   0.00037   3.43
25.32   0.00036   3.44
25.35   0.00035   3.45
25.38   0.00033   3.46
25.41   0.00032   3.47
25.44   0.00031   3.48
25.47   0.00030   3.49
25.50   0.00029   3.50
Draw a normal distribution and calculate probabilities                                        Back to Content
Area to the right

Mean                               15           There is a 74.75% chance that a score selected at random would
Sigma                               3           be 13 or more, or that 74.75% of all the scores will be 13 or more.
X1                                 13
Z1                       -0.666666667
Operator1           >=
P(X >= 13)               0.747507462
X2
Z2
Operator2
Probability

Insert the title for the diagram here:
      Mean = 15, sigma = 3




                                                                           5
                                                                           6
                                                                           8
                                                                          10

                                                                          13
                                                                          15

                                                                          19

                                                                          22
                                                                          24
                                                                          12


                                                                          17

                                                                          20
                                        Mean = 15, sigma = 3
          0.14000


          0.12000


          0.10000


          0.08000
   f(X)




                                                                                                    Remaining area

          0.06000                                                                                   Area for >= 13



          0.04000


          0.02000


          0.00000
                     5
                     6
                     7
                     8
                     5




                     9

                    11
                    11
                    12
                    13


                    16
                    17
                    18
                    18

                    20
                    21
                    22
                    23


                    25
                    10




                    14
                    15




                    19




                    24
                    25




          x         Remaining area       z      Area for >= 13
     4.50              0.00029          -3.50
     4.53              0.00030          -3.49
     4.56              0.00031          -3.48
     4.59              0.00032          -3.47
     4.62              0.00033          -3.46
     4.65              0.00035          -3.45
     4.68              0.00036          -3.44
     4.71              0.00037          -3.43
     4.74              0.00038          -3.42
     4.77              0.00040          -3.41
4.80   0.00041   -3.40
4.83   0.00042   -3.39
4.86   0.00044   -3.38
4.89   0.00045   -3.37
4.92   0.00047   -3.36
4.95   0.00049   -3.35
4.98   0.00050   -3.34
5.01   0.00052   -3.33
5.04   0.00054   -3.32
5.07   0.00056   -3.31
5.10   0.00057   -3.30
5.13   0.00059   -3.29
5.16   0.00061   -3.28
5.19   0.00063   -3.27
5.22   0.00065   -3.26
5.25   0.00068   -3.25
5.28   0.00070   -3.24
5.31   0.00072   -3.23
5.34   0.00075   -3.22
5.37   0.00077   -3.21
5.40   0.00079   -3.20
5.43   0.00082   -3.19
5.46   0.00085   -3.18
5.49   0.00087   -3.17
5.52   0.00090   -3.16
5.55   0.00093   -3.15
5.58   0.00096   -3.14
5.61   0.00099   -3.13
5.64   0.00102   -3.12
5.67   0.00106   -3.11
5.70   0.00109   -3.10
5.73   0.00112   -3.09
5.76   0.00116   -3.08
5.79   0.00119   -3.07
5.82   0.00123   -3.06
5.85   0.00127   -3.05
5.88   0.00131   -3.04
5.91   0.00135   -3.03
5.94   0.00139   -3.02
5.97   0.00143   -3.01
6.00   0.00148   -3.00
6.03   0.00152   -2.99
6.06   0.00157   -2.98
6.09   0.00162   -2.97
6.12   0.00166   -2.96
6.15   0.00171   -2.95
6.18   0.00177   -2.94
6.21   0.00182   -2.93
6.24   0.00187   -2.92
6.27   0.00193   -2.91
6.30   0.00198   -2.90
6.33   0.00204   -2.89
6.36   0.00210   -2.88
6.39   0.00216   -2.87
6.42   0.00223   -2.86
6.45   0.00229   -2.85
6.48   0.00236   -2.84
6.51   0.00242   -2.83
6.54   0.00249   -2.82
6.57   0.00257   -2.81
6.60   0.00264   -2.80
6.63   0.00271   -2.79
6.66   0.00279   -2.78
6.69   0.00287   -2.77
6.72   0.00295   -2.76
6.75   0.00303   -2.75
6.78   0.00312   -2.74
6.81   0.00320   -2.73
6.84   0.00329   -2.72
6.87   0.00338   -2.71
6.90   0.00347   -2.70
6.93   0.00357   -2.69
6.96   0.00367   -2.68
6.99   0.00377   -2.67
7.02   0.00387   -2.66
7.05   0.00397   -2.65
7.08   0.00408   -2.64
7.11   0.00419   -2.63
7.14   0.00430   -2.62
7.17   0.00441   -2.61
7.20   0.00453   -2.60
7.23   0.00465   -2.59
7.26   0.00477   -2.58
7.29   0.00489   -2.57
7.32   0.00502   -2.56
7.35   0.00515   -2.55
7.38   0.00528   -2.54
7.41   0.00542   -2.53
7.44   0.00556   -2.52
7.47   0.00570   -2.51
7.50   0.00584   -2.50
7.53   0.00599   -2.49
7.56   0.00614   -2.48
7.59   0.00629   -2.47
7.62   0.00645   -2.46
7.65   0.00661   -2.45
7.68   0.00678   -2.44
7.71   0.00694   -2.43
7.74   0.00711   -2.42
7.77   0.00729   -2.41
7.80   0.00746   -2.40
7.83   0.00765   -2.39
7.86   0.00783   -2.38
7.89   0.00802   -2.37
7.92   0.00821   -2.36
7.95   0.00841   -2.35
7.98   0.00861   -2.34
8.01   0.00881   -2.33
8.04   0.00902   -2.32
8.07   0.00923   -2.31
8.10   0.00944   -2.30
8.13   0.00966   -2.29
8.16   0.00988   -2.28
8.19   0.01011   -2.27
8.22   0.01034   -2.26
8.25   0.01058   -2.25
8.28   0.01082   -2.24
8.31   0.01106   -2.23
8.34   0.01131   -2.22
8.37   0.01157   -2.21
8.40   0.01182   -2.20
8.43   0.01209   -2.19
8.46   0.01235   -2.18
8.49   0.01263   -2.17
8.52   0.01290   -2.16
8.55   0.01318   -2.15
8.58   0.01347   -2.14
8.61   0.01376   -2.13
8.64   0.01406   -2.12
8.67   0.01436   -2.11
8.70   0.01466   -2.10
8.73   0.01497   -2.09
8.76   0.01529   -2.08
8.79   0.01561   -2.07
8.82   0.01593   -2.06
8.85   0.01626   -2.05
8.88   0.01660   -2.04
8.91   0.01694   -2.03
8.94   0.01729   -2.02
8.97   0.01764   -2.01
9.00   0.01800   -2.00
9.03   0.01836   -1.99
9.06   0.01873   -1.98
9.09   0.01910   -1.97
9.12   0.01948   -1.96
9.15   0.01986   -1.95
9.18   0.02026   -1.94
9.21   0.02065   -1.93
9.24   0.02105   -1.92
9.27   0.02146   -1.91
9.30   0.02187   -1.90
9.33   0.02229   -1.89
9.36   0.02271   -1.88
9.39   0.02314   -1.87
9.42   0.02358   -1.86
9.45   0.02402   -1.85
9.48   0.02447   -1.84
9.51   0.02492   -1.83
9.54   0.02538   -1.82
9.57   0.02585   -1.81
9.60   0.02632   -1.80
9.63   0.02679   -1.79
9.66   0.02728   -1.78
9.69   0.02776   -1.77
9.72   0.02826   -1.76
9.75   0.02876   -1.75
9.78   0.02927   -1.74
9.81   0.02978   -1.73
9.84    0.03030   -1.72
9.87    0.03082   -1.71
9.90    0.03135   -1.70
9.93    0.03189   -1.69
9.96    0.03243   -1.68
9.99    0.03298   -1.67
10.02   0.03353   -1.66
10.05   0.03409   -1.65
10.08   0.03465   -1.64
10.11   0.03522   -1.63
10.14   0.03580   -1.62
10.17   0.03638   -1.61
10.20   0.03697   -1.60
10.23   0.03757   -1.59
10.26   0.03817   -1.58
10.29   0.03877   -1.57
10.32   0.03939   -1.56
10.35   0.04000   -1.55
10.38   0.04063   -1.54
10.41   0.04125   -1.53
10.44   0.04189   -1.52
10.47   0.04253   -1.51
10.50   0.04317   -1.50
10.53   0.04382   -1.49
10.56   0.04448   -1.48
10.59   0.04514   -1.47
10.62   0.04581   -1.46
10.65   0.04648   -1.45
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10.71   0.04783   -1.43
10.74   0.04852   -1.42
10.77   0.04921   -1.41
10.80   0.04991   -1.40
10.83   0.05061   -1.39
10.86   0.05132   -1.38
10.89   0.05203   -1.37
10.92   0.05274   -1.36
10.95   0.05346   -1.35
10.98   0.05419   -1.34
11.01   0.05491   -1.33
11.04   0.05565   -1.32
11.07   0.05638   -1.31
11.10   0.05712   -1.30
11.13   0.05787   -1.29
11.16   0.05862   -1.28
11.19   0.05937   -1.27
11.22   0.06012   -1.26
11.25   0.06088   -1.25
11.28   0.06165   -1.24
11.31   0.06241   -1.23
11.34   0.06318   -1.22
11.37   0.06395   -1.21
11.40   0.06473   -1.20
11.43   0.06551   -1.19
11.46   0.06629   -1.18
11.49   0.06707   -1.17
11.52   0.06786   -1.16
11.55   0.06865   -1.15
11.58   0.06944   -1.14
11.61   0.07023   -1.13
11.64   0.07102   -1.12
11.67   0.07182   -1.11
11.70   0.07262   -1.10
11.73   0.07342   -1.09
11.76   0.07422   -1.08
11.79   0.07502   -1.07
11.82   0.07582   -1.06
11.85   0.07663   -1.05
11.88   0.07743   -1.04
11.91   0.07824   -1.03
11.94   0.07904   -1.02
11.97   0.07985   -1.01
12.00   0.08066   -1.00
12.03   0.08146   -0.99
12.06   0.08227   -0.98
12.09   0.08308   -0.97
12.12   0.08388   -0.96
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12.18   0.08549   -0.94
12.21   0.08629   -0.93
12.24   0.08710   -0.92
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12.30   0.08870   -0.90
12.33   0.08949   -0.89
12.36   0.09029   -0.88
12.39   0.09108   -0.87
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12.45   0.09266   -0.85
12.48   0.09345   -0.84
12.51   0.09423   -0.83
12.54   0.09501   -0.82
12.57   0.09579   -0.81
12.60   0.09656   -0.80
12.63   0.09733   -0.79
12.66   0.09810   -0.78
12.69   0.09886   -0.77
12.72   0.09962   -0.76
12.75   0.10038   -0.75
12.78   0.10113   -0.74
12.81   0.10188   -0.73
12.84   0.10262   -0.72
12.87   0.10335   -0.71
12.90   0.10408   -0.70
12.93   0.10481   -0.69
12.96   0.10553   -0.68
12.99   0.10625   -0.67
13.02   0.10695   -0.66   0.106954601
13.05   0.10766   -0.65   0.107657453
13.08   0.10835   -0.64   0.108354088
13.11   0.10904   -0.63   0.109044326
13.14   0.10973   -0.62   0.109727987
13.17   0.11040   -0.61   0.110404893
13.20   0.11107   -0.60   0.111074868
13.23   0.11174   -0.59   0.111737733
13.26   0.11239   -0.58   0.112393315
13.29   0.11304   -0.57   0.113041438
13.32   0.11368   -0.56    0.11368193
13.35   0.11431   -0.55   0.114314618
13.38   0.11494   -0.54   0.114939334
13.41   0.11556   -0.53   0.115555907
13.44   0.11616   -0.52   0.116164171
13.47   0.11676   -0.51    0.11676396
13.50   0.11736   -0.50   0.117355109
13.53   0.11794   -0.49   0.117937457
13.56   0.11851   -0.48   0.118510843
13.59   0.11908   -0.47   0.119075108
13.62   0.11963   -0.46   0.119630097
13.65   0.12018   -0.45   0.120175654
13.68   0.12071   -0.44   0.120711627
13.71   0.12124   -0.43   0.121237867
13.74   0.12175   -0.42   0.121754224
13.77   0.12226   -0.41   0.122260554
13.80   0.12276   -0.40   0.122756713
13.83   0.12324   -0.39   0.123242561
13.86   0.12372   -0.38    0.12371796
13.89   0.12418   -0.37   0.124182773
13.92   0.12464   -0.36   0.124636868
13.95   0.12508   -0.35   0.125080116
13.98   0.12551   -0.34   0.125512387
14.01   0.12593   -0.33   0.125933559
14.04   0.12634   -0.32   0.126343509
14.07   0.12674   -0.31   0.126742118
14.10   0.12713   -0.30   0.127129272
14.13   0.12750   -0.29   0.127504857
14.16   0.12787   -0.28   0.127868764
14.19   0.12822   -0.27   0.128220887
14.22   0.12856   -0.26   0.128561123
14.25   0.12889   -0.25   0.128889372
14.28   0.12921   -0.24   0.129205538
14.31   0.12951   -0.23   0.129509528
14.34   0.12980   -0.22   0.129801253
14.37   0.13008   -0.21   0.130080626
14.40   0.13035   -0.20   0.130347565
14.43   0.13060   -0.19    0.13060199
14.46   0.13084   -0.18   0.130843828
14.49   0.13107   -0.17   0.131073005
14.52   0.13129   -0.16   0.131289454
14.55   0.13149   -0.15    0.13149311
14.58   0.13168   -0.14   0.131683914
14.61   0.13186   -0.13   0.131861807
14.64   0.13203   -0.12   0.132026737
14.67   0.13218   -0.11   0.132178655
14.70   0.13232   -0.10   0.132317516
14.73   0.13244   -0.09   0.132443277
14.76   0.13256   -0.08   0.132555902
14.79   0.13266   -0.07   0.132655356
14.82   0.13274   -0.06    0.13274161
14.85   0.13281   -0.05   0.132814638
14.88   0.13287   -0.04   0.132874418
14.91   0.13292   -0.03   0.132920932
14.94   0.13295   -0.02   0.132954167
14.97   0.13297   -0.01   0.132974111
15.00   0.13298   0.00     0.13298076
15.03   0.13297   0.01    0.132974111
15.06   0.13295   0.02    0.132954167
15.09   0.13292   0.03    0.132920932
15.12   0.13287   0.04    0.132874418
15.15   0.13281   0.05    0.132814638
15.18   0.13274   0.06     0.13274161
15.21   0.13266   0.07    0.132655356
15.24   0.13256   0.08    0.132555902
15.27   0.13244   0.09    0.132443277
15.30   0.13232   0.10    0.132317516
15.33   0.13218   0.11    0.132178655
15.36   0.13203   0.12    0.132026737
15.39   0.13186   0.13    0.131861807
15.42   0.13168   0.14    0.131683914
15.45   0.13149   0.15     0.13149311
15.48   0.13129   0.16    0.131289454
15.51   0.13107   0.17    0.131073005
15.54   0.13084   0.18    0.130843828
15.57   0.13060   0.19     0.13060199
15.60   0.13035   0.20    0.130347565
15.63   0.13008   0.21    0.130080626
15.66   0.12980   0.22    0.129801253
15.69   0.12951   0.23    0.129509528
15.72   0.12921   0.24    0.129205538
15.75   0.12889   0.25    0.128889372
15.78   0.12856   0.26    0.128561123
15.81   0.12822   0.27    0.128220887
15.84   0.12787   0.28    0.127868764
15.87   0.12750   0.29    0.127504857
15.90   0.12713   0.30    0.127129272
15.93   0.12674   0.31    0.126742118
15.96   0.12634   0.32    0.126343509
15.99   0.12593   0.33    0.125933559
16.02   0.12551   0.34    0.125512387
16.05   0.12508   0.35    0.125080116
16.08   0.12464   0.36    0.124636868
16.11   0.12418   0.37    0.124182773
16.14   0.12372   0.38     0.12371796
16.17   0.12324   0.39    0.123242561
16.20   0.12276   0.40    0.122756713
16.23   0.12226   0.41    0.122260554
16.26   0.12175   0.42    0.121754224
16.29   0.12124   0.43    0.121237867
16.32   0.12071   0.44    0.120711627
16.35   0.12018   0.45    0.120175654
16.38   0.11963   0.46    0.119630097
16.41   0.11908   0.47    0.119075108
16.44   0.11851   0.48    0.118510843
16.47   0.11794   0.49    0.117937457
16.50   0.11736   0.50    0.117355109
16.53   0.11676   0.51     0.11676396
16.56   0.11616   0.52   0.116164171
16.59   0.11556   0.53   0.115555907
16.62   0.11494   0.54   0.114939334
16.65   0.11431   0.55   0.114314618
16.68   0.11368   0.56    0.11368193
16.71   0.11304   0.57   0.113041438
16.74   0.11239   0.58   0.112393315
16.77   0.11174   0.59   0.111737733
16.80   0.11107   0.60   0.111074868
16.83   0.11040   0.61   0.110404893
16.86   0.10973   0.62   0.109727987
16.89   0.10904   0.63   0.109044326
16.92   0.10835   0.64   0.108354088
16.95   0.10766   0.65   0.107657453
16.98   0.10695   0.66   0.106954601
17.01   0.10625   0.67   0.106245713
17.04   0.10553   0.68   0.105530969
17.07   0.10481   0.69   0.104810552
17.10   0.10408   0.70   0.104084644
17.13   0.10335   0.71   0.103353428
17.16   0.10262   0.72   0.102617087
17.19   0.10188   0.73   0.101875803
17.22   0.10113   0.74   0.101129761
17.25   0.10038   0.75   0.100379144
17.28   0.09962   0.76   0.099624135
17.31   0.09886   0.77   0.098864918
17.34   0.09810   0.78   0.098101677
17.37   0.09733   0.79   0.097334593
17.40   0.09656   0.80   0.096563851
17.43   0.09579   0.81   0.095789632
17.46   0.09501   0.82   0.095012119
17.49   0.09423   0.83   0.094231494
17.52   0.09345   0.84   0.093447937
17.55   0.09266   0.85   0.092661629
17.58   0.09187   0.86   0.091872749
17.61   0.09108   0.87   0.091081477
17.64   0.09029   0.88   0.090287991
17.67   0.08949   0.89   0.089492467
17.70   0.08870   0.90   0.088695083
17.73   0.08790   0.91   0.087896014
17.76   0.08710   0.92   0.087095434
17.79   0.08629   0.93   0.086293516
17.82   0.08549   0.94   0.085490431
17.85   0.08469   0.95   0.084686352
17.88   0.08388   0.96   0.083881447
17.91   0.08308   0.97   0.083075884
17.94   0.08227   0.98    0.08226983
17.97   0.08146   0.99    0.08146345
18.00   0.08066   1.00   0.080656908
18.03   0.07985   1.01   0.079850366
18.06   0.07904   1.02   0.079043984
18.09   0.07824   1.03   0.078237921
18.12   0.07743   1.04   0.077432335
18.15   0.07663   1.05    0.07662738
18.18   0.07582   1.06   0.075823211
18.21   0.07502   1.07   0.075019978
18.24   0.07422   1.08   0.074217833
18.27   0.07342   1.09   0.073416922
18.30   0.07262   1.10   0.072617392
18.33   0.07182   1.11   0.071819387
18.36   0.07102   1.12   0.071023049
18.39   0.07023   1.13   0.070228517
18.42   0.06944   1.14    0.06943593
18.45   0.06865   1.15   0.068645423
18.48   0.06786   1.16   0.067857129
18.51   0.06707   1.17   0.067071181
18.54   0.06629   1.18   0.066287706
18.57   0.06551   1.19   0.065506833
18.60   0.06473   1.20   0.064728685
18.63   0.06395   1.21   0.063953385
18.66   0.06318   1.22   0.063181053
18.69   0.06241   1.23   0.062411806
18.72   0.06165   1.24    0.06164576
18.75   0.06088   1.25   0.060883028
18.78   0.06012   1.26   0.060123721
18.81   0.05937   1.27   0.059367946
18.84   0.05862   1.28    0.05861581
18.87   0.05787   1.29   0.057867416
18.90   0.05712   1.30   0.057122864
18.93   0.05638   1.31   0.056382254
18.96   0.05565   1.32   0.055645681
18.99   0.05491   1.33   0.054913238
19.02   0.05419   1.34   0.054185018
19.05   0.05346   1.35   0.053461109
19.08   0.05274   1.36   0.052741597
19.11   0.05203   1.37   0.052026565
19.14   0.05132   1.38   0.051316096
19.17   0.05061   1.39   0.050610267
19.20   0.04991   1.40   0.049909155
19.23   0.04921   1.41   0.049212835
19.26   0.04852   1.42   0.048521377
19.29   0.04783   1.43    0.04783485
19.32   0.04715   1.44   0.047153322
19.35   0.04648   1.45   0.046476855
19.38   0.04581   1.46   0.045805513
19.41   0.04514   1.47   0.045139354
19.44   0.04448   1.48   0.044478435
19.47   0.04382   1.49    0.04382281
19.50   0.04317   1.50   0.043172532
19.53   0.04253   1.51    0.04252765
19.56   0.04189   1.52   0.041888212
19.59   0.04125   1.53   0.041254263
19.62   0.04063   1.54   0.040625846
19.65   0.04000   1.55      0.040003
19.68   0.03939   1.56   0.039385765
19.71   0.03877   1.57   0.038774176
19.74   0.03817   1.58   0.038168267
19.77   0.03757   1.59   0.037568069
19.80   0.03697   1.60   0.036973612
19.83   0.03638   1.61   0.036384922
19.86   0.03580   1.62   0.035802025
19.89   0.03522   1.63   0.035224944
19.92   0.03465   1.64   0.034653698
19.95   0.03409   1.65   0.034088308
19.98   0.03353   1.66   0.033528789
20.01   0.03298   1.67   0.032975157
20.04   0.03243   1.68   0.032427423
20.07   0.03189   1.69   0.031885599
20.10   0.03135   1.70   0.031349692
20.13   0.03082   1.71   0.030819711
20.16   0.03030   1.72    0.03029566
20.19   0.02978   1.73   0.029777541
20.22   0.02927   1.74   0.029265357
20.25   0.02876   1.75   0.028759106
20.28   0.02826   1.76   0.028258787
20.31   0.02776   1.77   0.027764395
20.34   0.02728   1.78   0.027275925
20.37   0.02679   1.79    0.02679337
20.40   0.02632   1.80   0.026316719
20.43   0.02585   1.81   0.025845964
20.46   0.02538   1.82   0.025381091
20.49   0.02492   1.83   0.024922087
20.52   0.02447   1.84   0.024468938
20.55   0.02402   1.85   0.024021625
20.58   0.02358   1.86   0.023580131
20.61   0.02314   1.87   0.023144437
20.64   0.02271   1.88   0.022714522
20.67   0.02229   1.89   0.022290364
20.70   0.02187   1.90   0.021871938
20.73   0.02146   1.91   0.021459221
20.76   0.02105   1.92   0.021052187
20.79   0.02065   1.93   0.020650808
20.82   0.02026   1.94   0.020255056
20.85   0.01986   1.95   0.019864902
20.88   0.01948   1.96   0.019480315
20.91   0.01910   1.97   0.019101263
20.94   0.01873   1.98   0.018727714
20.97   0.01836   1.99   0.018359634
21.00   0.01800   2.00   0.017996989
21.03   0.01764   2.01   0.017639743
21.06   0.01729   2.02   0.017287859
21.09   0.01694   2.03     0.0169413
21.12   0.01660   2.04   0.016600029
21.15   0.01626   2.05   0.016264006
21.18   0.01593   2.06   0.015933192
21.21   0.01561   2.07   0.015607545
21.24   0.01529   2.08   0.015287025
21.27   0.01497   2.09   0.014971591
21.30   0.01466   2.10   0.014661199
21.33   0.01436   2.11   0.014355806
21.36   0.01406   2.12   0.014055369
21.39   0.01376   2.13   0.013759843
21.42   0.01347   2.14   0.013469185
21.45   0.01318   2.15   0.013183347
21.48   0.01290   2.16   0.012902285
21.51   0.01263   2.17   0.012625953
21.54   0.01235   2.18   0.012354303
21.57   0.01209   2.19    0.01208729
21.60   0.01182   2.20   0.011824864
21.63   0.01157   2.21    0.01156698
21.66   0.01131   2.22   0.011313588
21.69   0.01106   2.23    0.01106464
21.72   0.01082   2.24   0.010820089
21.75   0.01058   2.25   0.010579884
21.78   0.01034   2.26   0.010343977
21.81   0.01011   2.27    0.01011232
21.84   0.00988   2.28   0.009884862
21.87   0.00966   2.29   0.009661554
21.90   0.00944   2.30   0.009442346
21.93   0.00923   2.31   0.009227189
21.96   0.00902   2.32   0.009016033
21.99   0.00881   2.33   0.008808828
22.02   0.00861   2.34   0.008605525
22.05   0.00841   2.35   0.008406073
22.08   0.00821   2.36   0.008210423
22.11   0.00802   2.37   0.008018525
22.14   0.00783   2.38   0.007830328
22.17   0.00765   2.39   0.007645785
22.20   0.00746   2.40   0.007464843
22.23   0.00729   2.41   0.007287456
22.26   0.00711   2.42   0.007113572
22.29   0.00694   2.43   0.006943142
22.32   0.00678   2.44   0.006776119
22.35   0.00661   2.45   0.006612451
22.38   0.00645   2.46   0.006452092
22.41   0.00629   2.47   0.006294992
22.44   0.00614   2.48   0.006141104
22.47   0.00599   2.49   0.005990378
22.50   0.00584   2.50   0.005842767
22.53   0.00570   2.51   0.005698223
22.56   0.00556   2.52     0.0055567
22.59   0.00542   2.53    0.00541815
22.62   0.00528   2.54   0.005282526
22.65   0.00515   2.55   0.005149782
22.68   0.00502   2.56   0.005019872
22.71   0.00489   2.57    0.00489275
22.74   0.00477   2.58    0.00476837
22.77   0.00465   2.59   0.004646687
22.80   0.00453   2.60   0.004527656
22.83   0.00441   2.61   0.004411234
22.86   0.00430   2.62   0.004297375
22.89   0.00419   2.63   0.004186037
22.92   0.00408   2.64   0.004077175
22.95   0.00397   2.65   0.003970748
22.98   0.00387   2.66   0.003866712
23.01   0.00377   2.67   0.003765025
23.04   0.00367   2.68   0.003665646
23.07   0.00357   2.69   0.003568533
23.10   0.00347   2.70   0.003473645
23.13   0.00338   2.71   0.003380942
23.16   0.00329   2.72   0.003290385
23.19   0.00320   2.73   0.003201932
23.22   0.00312   2.74   0.003115546
23.25   0.00303   2.75   0.003031188
23.28   0.00295   2.76   0.002948818
23.31   0.00287   2.77     0.0028684
23.34   0.00279   2.78   0.002789896
23.37   0.00271   2.79    0.00271327
23.40   0.00264   2.80   0.002638484
23.43   0.00257   2.81   0.002565503
23.46   0.00249   2.82   0.002494291
23.49   0.00242   2.83   0.002424813
23.52   0.00236   2.84   0.002357035
23.55   0.00229   2.85   0.002290922
23.58   0.00223   2.86   0.002226441
23.61   0.00216   2.87   0.002163559
23.64   0.00210   2.88   0.002102242
23.67   0.00204   2.89   0.002042459
23.70   0.00198   2.90   0.001984177
23.73   0.00193   2.91   0.001927366
23.76   0.00187   2.92   0.001871995
23.79   0.00182   2.93   0.001818032
23.82   0.00177   2.94   0.001765448
23.85   0.00171   2.95   0.001714214
23.88   0.00166   2.96     0.0016643
23.91   0.00162   2.97   0.001615678
23.94   0.00157   2.98   0.001568319
23.97   0.00152   2.99   0.001522197
24.00   0.00148   3.00   0.001477283
24.03   0.00143   3.01   0.001433551
24.06   0.00139   3.02   0.001390974
24.09   0.00135   3.03   0.001349527
24.12   0.00131   3.04   0.001309185
24.15   0.00127   3.05   0.001269921
24.18   0.00123   3.06   0.001231711
24.21   0.00119   3.07   0.001194532
24.24   0.00116   3.08   0.001158359
24.27   0.00112   3.09   0.001123169
24.30   0.00109   3.10    0.00108894
24.33   0.00106   3.11   0.001055648
24.36   0.00102   3.12   0.001023271
24.39   0.00099   3.13   0.000991788
24.42   0.00096   3.14   0.000961178
24.45   0.00093   3.15   0.000931419
24.48   0.00090   3.16   0.000902492
24.51   0.00087   3.17   0.000874375
24.54   0.00085   3.18    0.00084705
24.57   0.00082   3.19   0.000820497
24.60   0.00079   3.20   0.000794696
24.63   0.00077   3.21    0.00076963
24.66   0.00075   3.22    0.00074528
24.69   0.00072   3.23   0.000721628
24.72   0.00070   3.24   0.000698657
24.75   0.00068   3.25   0.000676349
24.78   0.00065   3.26   0.000654689
24.81   0.00063   3.27   0.000633658
24.84   0.00061   3.28   0.000613242
24.87   0.00059   3.29   0.000593424
24.90   0.00057   3.30    0.00057419
24.93   0.00056   3.31   0.000555523
24.96   0.00054   3.32   0.000537409
24.99   0.00052   3.33   0.000519834
25.02   0.00050   3.34   0.000502784
25.05   0.00049   3.35   0.000486244
25.08   0.00047   3.36   0.000470201
25.11   0.00045   3.37   0.000454642
25.14   0.00044   3.38   0.000439554
25.17   0.00042   3.39   0.000424924
25.20   0.00041   3.40    0.00041074
25.23   0.00040   3.41   0.000396989
25.26   0.00038   3.42   0.000383661
25.29   0.00037   3.43   0.000370743
25.32   0.00036   3.44   0.000358224
25.35   0.00035   3.45   0.000346094
25.38   0.00033   3.46    0.00033434
25.41   0.00032   3.47   0.000322954
25.44   0.00031   3.48   0.000311924
25.47   0.00030   3.49   0.000301241
25.50   0.00029   3.50   0.000290894
Draw a normal distribution and calculate probabilities                                        Back to Content
Area between two values

Mean                                   15           There is a 58.89% chance that the
Sigma                                   3           score selected at random will be
X1                                     13           between 13 and 18, or that 58.89% of
Z1                           -0.666666667           all scores will be between 13 and 18.
Operator1               >=
P(X >= 13)                    0.252492538
X2                                     18
Z2                                      1
Operator2               <=
P(13>= X <= 18)               0.588852209

Insert the title for the diagram here:
           Mean = 15, sigma = 3




                                                           6
                                                           8
                                                           9
                                                           5




                                                          11

                                                          14
                                                          15

                                                          18

                                                          21
                                                          23
                                                          12


                                                          17

                                                          20


                                                          24
                                  Mean = 15, sigma = 3
            0.14000

            0.12000

            0.10000

            0.08000
     f(X)




                                                                                    Remaining area

            0.06000                                                                 Area for>=13 and <=18


            0.04000

            0.02000

            0.00000
                       5
                       6
                       7
                       8
                       9
                      10
                      11
                      12
                      13
                      14
                      15
                      16
                      17
                      18
                      19
                      20
                      21
                      22
                      23
                      24
                      25




              x          Remaining area      z      Area for>=13 and <=18
             4.50           0.00029         -3.50
             4.53           0.00030         -3.49
             4.56           0.00031         -3.48
             4.59           0.00032         -3.47
             4.62           0.00033         -3.46
             4.65           0.00035         -3.45
             4.68           0.00036         -3.44
             4.71           0.00037         -3.43
             4.74           0.00038         -3.42
             4.77           0.00040         -3.41
4.80   0.00041   -3.40
4.83   0.00042   -3.39
4.86   0.00044   -3.38
4.89   0.00045   -3.37
4.92   0.00047   -3.36
4.95   0.00049   -3.35
4.98   0.00050   -3.34
5.01   0.00052   -3.33
5.04   0.00054   -3.32
5.07   0.00056   -3.31
5.10   0.00057   -3.30
5.13   0.00059   -3.29
5.16   0.00061   -3.28
5.19   0.00063   -3.27
5.22   0.00065   -3.26
5.25   0.00068   -3.25
5.28   0.00070   -3.24
5.31   0.00072   -3.23
5.34   0.00075   -3.22
5.37   0.00077   -3.21
5.40   0.00079   -3.20
5.43   0.00082   -3.19
5.46   0.00085   -3.18
5.49   0.00087   -3.17
5.52   0.00090   -3.16
5.55   0.00093   -3.15
5.58   0.00096   -3.14
5.61   0.00099   -3.13
5.64   0.00102   -3.12
5.67   0.00106   -3.11
5.70   0.00109   -3.10
5.73   0.00112   -3.09
5.76   0.00116   -3.08
5.79   0.00119   -3.07
5.82   0.00123   -3.06
5.85   0.00127   -3.05
5.88   0.00131   -3.04
5.91   0.00135   -3.03
5.94   0.00139   -3.02
5.97   0.00143   -3.01
6.00   0.00148   -3.00
6.03   0.00152   -2.99
6.06   0.00157   -2.98
6.09   0.00162   -2.97
6.12   0.00166   -2.96
6.15   0.00171   -2.95
6.18   0.00177   -2.94
6.21   0.00182   -2.93
6.24   0.00187   -2.92
6.27   0.00193   -2.91
6.30   0.00198   -2.90
6.33   0.00204   -2.89
6.36   0.00210   -2.88
6.39   0.00216   -2.87
6.42   0.00223   -2.86
6.45   0.00229   -2.85
6.48   0.00236   -2.84
6.51   0.00242   -2.83
6.54   0.00249   -2.82
6.57   0.00257   -2.81
6.60   0.00264   -2.80
6.63   0.00271   -2.79
6.66   0.00279   -2.78
6.69   0.00287   -2.77
6.72   0.00295   -2.76
6.75   0.00303   -2.75
6.78   0.00312   -2.74
6.81   0.00320   -2.73
6.84   0.00329   -2.72
6.87   0.00338   -2.71
6.90   0.00347   -2.70
6.93   0.00357   -2.69
6.96   0.00367   -2.68
6.99   0.00377   -2.67
7.02   0.00387   -2.66
7.05   0.00397   -2.65
7.08   0.00408   -2.64
7.11   0.00419   -2.63
7.14   0.00430   -2.62
7.17   0.00441   -2.61
7.20   0.00453   -2.60
7.23   0.00465   -2.59
7.26   0.00477   -2.58
7.29   0.00489   -2.57
7.32   0.00502   -2.56
7.35   0.00515   -2.55
7.38   0.00528   -2.54
7.41   0.00542   -2.53
7.44   0.00556   -2.52
7.47   0.00570   -2.51
7.50   0.00584   -2.50
7.53   0.00599   -2.49
7.56   0.00614   -2.48
7.59   0.00629   -2.47
7.62   0.00645   -2.46
7.65   0.00661   -2.45
7.68   0.00678   -2.44
7.71   0.00694   -2.43
7.74   0.00711   -2.42
7.77   0.00729   -2.41
7.80   0.00746   -2.40
7.83   0.00765   -2.39
7.86   0.00783   -2.38
7.89   0.00802   -2.37
7.92   0.00821   -2.36
7.95   0.00841   -2.35
7.98   0.00861   -2.34
8.01   0.00881   -2.33
8.04   0.00902   -2.32
8.07   0.00923   -2.31
8.10   0.00944   -2.30
8.13   0.00966   -2.29
8.16   0.00988   -2.28
8.19   0.01011   -2.27
8.22   0.01034   -2.26
8.25   0.01058   -2.25
8.28   0.01082   -2.24
8.31   0.01106   -2.23
8.34   0.01131   -2.22
8.37   0.01157   -2.21
8.40   0.01182   -2.20
8.43   0.01209   -2.19
8.46   0.01235   -2.18
8.49   0.01263   -2.17
8.52   0.01290   -2.16
8.55   0.01318   -2.15
8.58   0.01347   -2.14
8.61   0.01376   -2.13
8.64   0.01406   -2.12
8.67   0.01436   -2.11
8.70   0.01466   -2.10
8.73   0.01497   -2.09
8.76   0.01529   -2.08
8.79   0.01561   -2.07
8.82   0.01593   -2.06
8.85   0.01626   -2.05
8.88   0.01660   -2.04
8.91   0.01694   -2.03
8.94   0.01729   -2.02
8.97   0.01764   -2.01
9.00   0.01800   -2.00
9.03   0.01836   -1.99
9.06   0.01873   -1.98
9.09   0.01910   -1.97
9.12   0.01948   -1.96
9.15   0.01986   -1.95
9.18   0.02026   -1.94
9.21   0.02065   -1.93
9.24   0.02105   -1.92
9.27   0.02146   -1.91
9.30   0.02187   -1.90
9.33   0.02229   -1.89
9.36   0.02271   -1.88
9.39   0.02314   -1.87
9.42   0.02358   -1.86
9.45   0.02402   -1.85
9.48   0.02447   -1.84
9.51   0.02492   -1.83
9.54   0.02538   -1.82
9.57   0.02585   -1.81
9.60   0.02632   -1.80
9.63   0.02679   -1.79
9.66   0.02728   -1.78
9.69   0.02776   -1.77
9.72   0.02826   -1.76
9.75   0.02876   -1.75
9.78   0.02927   -1.74
9.81   0.02978   -1.73
9.84    0.03030   -1.72
9.87    0.03082   -1.71
9.90    0.03135   -1.70
9.93    0.03189   -1.69
9.96    0.03243   -1.68
9.99    0.03298   -1.67
10.02   0.03353   -1.66
10.05   0.03409   -1.65
10.08   0.03465   -1.64
10.11   0.03522   -1.63
10.14   0.03580   -1.62
10.17   0.03638   -1.61
10.20   0.03697   -1.60
10.23   0.03757   -1.59
10.26   0.03817   -1.58
10.29   0.03877   -1.57
10.32   0.03939   -1.56
10.35   0.04000   -1.55
10.38   0.04063   -1.54
10.41   0.04125   -1.53
10.44   0.04189   -1.52
10.47   0.04253   -1.51
10.50   0.04317   -1.50
10.53   0.04382   -1.49
10.56   0.04448   -1.48
10.59   0.04514   -1.47
10.62   0.04581   -1.46
10.65   0.04648   -1.45
10.68   0.04715   -1.44
10.71   0.04783   -1.43
10.74   0.04852   -1.42
10.77   0.04921   -1.41
10.80   0.04991   -1.40
10.83   0.05061   -1.39
10.86   0.05132   -1.38
10.89   0.05203   -1.37
10.92   0.05274   -1.36
10.95   0.05346   -1.35
10.98   0.05419   -1.34
11.01   0.05491   -1.33
11.04   0.05565   -1.32
11.07   0.05638   -1.31
11.10   0.05712   -1.30
11.13   0.05787   -1.29
11.16   0.05862   -1.28
11.19   0.05937   -1.27
11.22   0.06012   -1.26
11.25   0.06088   -1.25
11.28   0.06165   -1.24
11.31   0.06241   -1.23
11.34   0.06318   -1.22
11.37   0.06395   -1.21
11.40   0.06473   -1.20
11.43   0.06551   -1.19
11.46   0.06629   -1.18
11.49   0.06707   -1.17
11.52   0.06786   -1.16
11.55   0.06865   -1.15
11.58   0.06944   -1.14
11.61   0.07023   -1.13
11.64   0.07102   -1.12
11.67   0.07182   -1.11
11.70   0.07262   -1.10
11.73   0.07342   -1.09
11.76   0.07422   -1.08
11.79   0.07502   -1.07
11.82   0.07582   -1.06
11.85   0.07663   -1.05
11.88   0.07743   -1.04
11.91   0.07824   -1.03
11.94   0.07904   -1.02
11.97   0.07985   -1.01
12.00   0.08066   -1.00
12.03   0.08146   -0.99
12.06   0.08227   -0.98
12.09   0.08308   -0.97
12.12   0.08388   -0.96
12.15   0.08469   -0.95
12.18   0.08549   -0.94
12.21   0.08629   -0.93
12.24   0.08710   -0.92
12.27   0.08790   -0.91
12.30   0.08870   -0.90
12.33   0.08949   -0.89
12.36   0.09029   -0.88
12.39   0.09108   -0.87
12.42   0.09187   -0.86
12.45   0.09266   -0.85
12.48   0.09345   -0.84
12.51   0.09423   -0.83
12.54   0.09501   -0.82
12.57   0.09579   -0.81
12.60   0.09656   -0.80
12.63   0.09733   -0.79
12.66   0.09810   -0.78
12.69   0.09886   -0.77
12.72   0.09962   -0.76
12.75   0.10038   -0.75
12.78   0.10113   -0.74
12.81   0.10188   -0.73
12.84   0.10262   -0.72
12.87   0.10335   -0.71
12.90   0.10408   -0.70
12.93   0.10481   -0.69
12.96   0.10553   -0.68
12.99   0.10625   -0.67
13.02   0.10695   -0.66   0.106954601
13.05   0.10766   -0.65   0.107657453
13.08   0.10835   -0.64   0.108354088
13.11   0.10904   -0.63   0.109044326
13.14   0.10973   -0.62   0.109727987
13.17   0.11040   -0.61   0.110404893
13.20   0.11107   -0.60   0.111074868
13.23   0.11174   -0.59   0.111737733
13.26   0.11239   -0.58   0.112393315
13.29   0.11304   -0.57   0.113041438
13.32   0.11368   -0.56    0.11368193
13.35   0.11431   -0.55   0.114314618
13.38   0.11494   -0.54   0.114939334
13.41   0.11556   -0.53   0.115555907
13.44   0.11616   -0.52   0.116164171
13.47   0.11676   -0.51    0.11676396
13.50   0.11736   -0.50   0.117355109
13.53   0.11794   -0.49   0.117937457
13.56   0.11851   -0.48   0.118510843
13.59   0.11908   -0.47   0.119075108
13.62   0.11963   -0.46   0.119630097
13.65   0.12018   -0.45   0.120175654
13.68   0.12071   -0.44   0.120711627
13.71   0.12124   -0.43   0.121237867
13.74   0.12175   -0.42   0.121754224
13.77   0.12226   -0.41   0.122260554
13.80   0.12276   -0.40   0.122756713
13.83   0.12324   -0.39   0.123242561
13.86   0.12372   -0.38    0.12371796
13.89   0.12418   -0.37   0.124182773
13.92   0.12464   -0.36   0.124636868
13.95   0.12508   -0.35   0.125080116
13.98   0.12551   -0.34   0.125512387
14.01   0.12593   -0.33   0.125933559
14.04   0.12634   -0.32   0.126343509
14.07   0.12674   -0.31   0.126742118
14.10   0.12713   -0.30   0.127129272
14.13   0.12750   -0.29   0.127504857
14.16   0.12787   -0.28   0.127868764
14.19   0.12822   -0.27   0.128220887
14.22   0.12856   -0.26   0.128561123
14.25   0.12889   -0.25   0.128889372
14.28   0.12921   -0.24   0.129205538
14.31   0.12951   -0.23   0.129509528
14.34   0.12980   -0.22   0.129801253
14.37   0.13008   -0.21   0.130080626
14.40   0.13035   -0.20   0.130347565
14.43   0.13060   -0.19    0.13060199
14.46   0.13084   -0.18   0.130843828
14.49   0.13107   -0.17   0.131073005
14.52   0.13129   -0.16   0.131289454
14.55   0.13149   -0.15    0.13149311
14.58   0.13168   -0.14   0.131683914
14.61   0.13186   -0.13   0.131861807
14.64   0.13203   -0.12   0.132026737
14.67   0.13218   -0.11   0.132178655
14.70   0.13232   -0.10   0.132317516
14.73   0.13244   -0.09   0.132443277
14.76   0.13256   -0.08   0.132555902
14.79   0.13266   -0.07   0.132655356
14.82   0.13274   -0.06    0.13274161
14.85   0.13281   -0.05   0.132814638
14.88   0.13287   -0.04   0.132874418
14.91   0.13292   -0.03   0.132920932
14.94   0.13295   -0.02   0.132954167
14.97   0.13297   -0.01   0.132974111
15.00   0.13298   0.00     0.13298076
15.03   0.13297   0.01    0.132974111
15.06   0.13295   0.02    0.132954167
15.09   0.13292   0.03    0.132920932
15.12   0.13287   0.04    0.132874418
15.15   0.13281   0.05    0.132814638
15.18   0.13274   0.06     0.13274161
15.21   0.13266   0.07    0.132655356
15.24   0.13256   0.08    0.132555902
15.27   0.13244   0.09    0.132443277
15.30   0.13232   0.10    0.132317516
15.33   0.13218   0.11    0.132178655
15.36   0.13203   0.12    0.132026737
15.39   0.13186   0.13    0.131861807
15.42   0.13168   0.14    0.131683914
15.45   0.13149   0.15     0.13149311
15.48   0.13129   0.16    0.131289454
15.51   0.13107   0.17    0.131073005
15.54   0.13084   0.18    0.130843828
15.57   0.13060   0.19     0.13060199
15.60   0.13035   0.20    0.130347565
15.63   0.13008   0.21    0.130080626
15.66   0.12980   0.22    0.129801253
15.69   0.12951   0.23    0.129509528
15.72   0.12921   0.24    0.129205538
15.75   0.12889   0.25    0.128889372
15.78   0.12856   0.26    0.128561123
15.81   0.12822   0.27    0.128220887
15.84   0.12787   0.28    0.127868764
15.87   0.12750   0.29    0.127504857
15.90   0.12713   0.30    0.127129272
15.93   0.12674   0.31    0.126742118
15.96   0.12634   0.32    0.126343509
15.99   0.12593   0.33    0.125933559
16.02   0.12551   0.34    0.125512387
16.05   0.12508   0.35    0.125080116
16.08   0.12464   0.36    0.124636868
16.11   0.12418   0.37    0.124182773
16.14   0.12372   0.38     0.12371796
16.17   0.12324   0.39    0.123242561
16.20   0.12276   0.40    0.122756713
16.23   0.12226   0.41    0.122260554
16.26   0.12175   0.42    0.121754224
16.29   0.12124   0.43    0.121237867
16.32   0.12071   0.44    0.120711627
16.35   0.12018   0.45    0.120175654
16.38   0.11963   0.46    0.119630097
16.41   0.11908   0.47    0.119075108
16.44   0.11851   0.48    0.118510843
16.47   0.11794   0.49    0.117937457
16.50   0.11736   0.50    0.117355109
16.53   0.11676   0.51     0.11676396
16.56   0.11616   0.52   0.116164171
16.59   0.11556   0.53   0.115555907
16.62   0.11494   0.54   0.114939334
16.65   0.11431   0.55   0.114314618
16.68   0.11368   0.56    0.11368193
16.71   0.11304   0.57   0.113041438
16.74   0.11239   0.58   0.112393315
16.77   0.11174   0.59   0.111737733
16.80   0.11107   0.60   0.111074868
16.83   0.11040   0.61   0.110404893
16.86   0.10973   0.62   0.109727987
16.89   0.10904   0.63   0.109044326
16.92   0.10835   0.64   0.108354088
16.95   0.10766   0.65   0.107657453
16.98   0.10695   0.66   0.106954601
17.01   0.10625   0.67   0.106245713
17.04   0.10553   0.68   0.105530969
17.07   0.10481   0.69   0.104810552
17.10   0.10408   0.70   0.104084644
17.13   0.10335   0.71   0.103353428
17.16   0.10262   0.72   0.102617087
17.19   0.10188   0.73   0.101875803
17.22   0.10113   0.74   0.101129761
17.25   0.10038   0.75   0.100379144
17.28   0.09962   0.76   0.099624135
17.31   0.09886   0.77   0.098864918
17.34   0.09810   0.78   0.098101677
17.37   0.09733   0.79   0.097334593
17.40   0.09656   0.80   0.096563851
17.43   0.09579   0.81   0.095789632
17.46   0.09501   0.82   0.095012119
17.49   0.09423   0.83   0.094231494
17.52   0.09345   0.84   0.093447937
17.55   0.09266   0.85   0.092661629
17.58   0.09187   0.86   0.091872749
17.61   0.09108   0.87   0.091081477
17.64   0.09029   0.88   0.090287991
17.67   0.08949   0.89   0.089492467
17.70   0.08870   0.90   0.088695083
17.73   0.08790   0.91   0.087896014
17.76   0.08710   0.92   0.087095434
17.79   0.08629   0.93   0.086293516
17.82   0.08549   0.94   0.085490431
17.85   0.08469   0.95   0.084686352
17.88   0.08388   0.96   0.083881447
17.91   0.08308   0.97   0.083075884
17.94   0.08227   0.98    0.08226983
17.97   0.08146   0.99    0.08146345
18.00   0.08066   1.00   0.080656908
18.03   0.07985   1.01
18.06   0.07904   1.02
18.09   0.07824   1.03
18.12   0.07743   1.04
18.15   0.07663   1.05
18.18   0.07582   1.06
18.21   0.07502   1.07
18.24   0.07422   1.08
18.27   0.07342   1.09
18.30   0.07262   1.10
18.33   0.07182   1.11
18.36   0.07102   1.12
18.39   0.07023   1.13
18.42   0.06944   1.14
18.45   0.06865   1.15
18.48   0.06786   1.16
18.51   0.06707   1.17
18.54   0.06629   1.18
18.57   0.06551   1.19
18.60   0.06473   1.20
18.63   0.06395   1.21
18.66   0.06318   1.22
18.69   0.06241   1.23
18.72   0.06165   1.24
18.75   0.06088   1.25
18.78   0.06012   1.26
18.81   0.05937   1.27
18.84   0.05862   1.28
18.87   0.05787   1.29
18.90   0.05712   1.30
18.93   0.05638   1.31
18.96   0.05565   1.32
18.99   0.05491   1.33
19.02   0.05419   1.34
19.05   0.05346   1.35
19.08   0.05274   1.36
19.11   0.05203   1.37
19.14   0.05132   1.38
19.17   0.05061   1.39
19.20   0.04991   1.40
19.23   0.04921   1.41
19.26   0.04852   1.42
19.29   0.04783   1.43
19.32   0.04715   1.44
19.35   0.04648   1.45
19.38   0.04581   1.46
19.41   0.04514   1.47
19.44   0.04448   1.48
19.47   0.04382   1.49
19.50   0.04317   1.50
19.53   0.04253   1.51
19.56   0.04189   1.52
19.59   0.04125   1.53
19.62   0.04063   1.54
19.65   0.04000   1.55
19.68   0.03939   1.56
19.71   0.03877   1.57
19.74   0.03817   1.58
19.77   0.03757   1.59
19.80   0.03697   1.60
19.83   0.03638   1.61
19.86   0.03580   1.62
19.89   0.03522   1.63
19.92   0.03465   1.64
19.95   0.03409   1.65
19.98   0.03353   1.66
20.01   0.03298   1.67
20.04   0.03243   1.68
20.07   0.03189   1.69
20.10   0.03135   1.70
20.13   0.03082   1.71
20.16   0.03030   1.72
20.19   0.02978   1.73
20.22   0.02927   1.74
20.25   0.02876   1.75
20.28   0.02826   1.76
20.31   0.02776   1.77
20.34   0.02728   1.78
20.37   0.02679   1.79
20.40   0.02632   1.80
20.43   0.02585   1.81
20.46   0.02538   1.82
20.49   0.02492   1.83
20.52   0.02447   1.84
20.55   0.02402   1.85
20.58   0.02358   1.86
20.61   0.02314   1.87
20.64   0.02271   1.88
20.67   0.02229   1.89
20.70   0.02187   1.90
20.73   0.02146   1.91
20.76   0.02105   1.92
20.79   0.02065   1.93
20.82   0.02026   1.94
20.85   0.01986   1.95
20.88   0.01948   1.96
20.91   0.01910   1.97
20.94   0.01873   1.98
20.97   0.01836   1.99
21.00   0.01800   2.00
21.03   0.01764   2.01
21.06   0.01729   2.02
21.09   0.01694   2.03
21.12   0.01660   2.04
21.15   0.01626   2.05
21.18   0.01593   2.06
21.21   0.01561   2.07
21.24   0.01529   2.08
21.27   0.01497   2.09
21.30   0.01466   2.10
21.33   0.01436   2.11
21.36   0.01406   2.12
21.39   0.01376   2.13
21.42   0.01347   2.14
21.45   0.01318   2.15
21.48   0.01290   2.16
21.51   0.01263   2.17
21.54   0.01235   2.18
21.57   0.01209   2.19
21.60   0.01182   2.20
21.63   0.01157   2.21
21.66   0.01131   2.22
21.69   0.01106   2.23
21.72   0.01082   2.24
21.75   0.01058   2.25
21.78   0.01034   2.26
21.81   0.01011   2.27
21.84   0.00988   2.28
21.87   0.00966   2.29
21.90   0.00944   2.30
21.93   0.00923   2.31
21.96   0.00902   2.32
21.99   0.00881   2.33
22.02   0.00861   2.34
22.05   0.00841   2.35
22.08   0.00821   2.36
22.11   0.00802   2.37
22.14   0.00783   2.38
22.17   0.00765   2.39
22.20   0.00746   2.40
22.23   0.00729   2.41
22.26   0.00711   2.42
22.29   0.00694   2.43
22.32   0.00678   2.44
22.35   0.00661   2.45
22.38   0.00645   2.46
22.41   0.00629   2.47
22.44   0.00614   2.48
22.47   0.00599   2.49
22.50   0.00584   2.50
22.53   0.00570   2.51
22.56   0.00556   2.52
22.59   0.00542   2.53
22.62   0.00528   2.54
22.65   0.00515   2.55
22.68   0.00502   2.56
22.71   0.00489   2.57
22.74   0.00477   2.58
22.77   0.00465   2.59
22.80   0.00453   2.60
22.83   0.00441   2.61
22.86   0.00430   2.62
22.89   0.00419   2.63
22.92   0.00408   2.64
22.95   0.00397   2.65
22.98   0.00387   2.66
23.01   0.00377   2.67
23.04   0.00367   2.68
23.07   0.00357   2.69
23.10   0.00347   2.70
23.13   0.00338   2.71
23.16   0.00329   2.72
23.19   0.00320   2.73
23.22   0.00312   2.74
23.25   0.00303   2.75
23.28   0.00295   2.76
23.31   0.00287   2.77
23.34   0.00279   2.78
23.37   0.00271   2.79
23.40   0.00264   2.80
23.43   0.00257   2.81
23.46   0.00249   2.82
23.49   0.00242   2.83
23.52   0.00236   2.84
23.55   0.00229   2.85
23.58   0.00223   2.86
23.61   0.00216   2.87
23.64   0.00210   2.88
23.67   0.00204   2.89
23.70   0.00198   2.90
23.73   0.00193   2.91
23.76   0.00187   2.92
23.79   0.00182   2.93
23.82   0.00177   2.94
23.85   0.00171   2.95
23.88   0.00166   2.96
23.91   0.00162   2.97
23.94   0.00157   2.98
23.97   0.00152   2.99
24.00   0.00148   3.00
24.03   0.00143   3.01
24.06   0.00139   3.02
24.09   0.00135   3.03
24.12   0.00131   3.04
24.15   0.00127   3.05
24.18   0.00123   3.06
24.21   0.00119   3.07
24.24   0.00116   3.08
24.27   0.00112   3.09
24.30   0.00109   3.10
24.33   0.00106   3.11
24.36   0.00102   3.12
24.39   0.00099   3.13
24.42   0.00096   3.14
24.45   0.00093   3.15
24.48   0.00090   3.16
24.51   0.00087   3.17
24.54   0.00085   3.18
24.57   0.00082   3.19
24.60   0.00079   3.20
24.63   0.00077   3.21
24.66   0.00075   3.22
24.69   0.00072   3.23
24.72   0.00070   3.24
24.75   0.00068   3.25
24.78   0.00065   3.26
24.81   0.00063   3.27
24.84   0.00061   3.28
24.87   0.00059   3.29
24.90   0.00057   3.30
24.93   0.00056   3.31
24.96   0.00054   3.32
24.99   0.00052   3.33
25.02   0.00050   3.34
25.05   0.00049   3.35
25.08   0.00047   3.36
25.11   0.00045   3.37
25.14   0.00044   3.38
25.17   0.00042   3.39
25.20   0.00041   3.40
25.23   0.00040   3.41
25.26   0.00038   3.42
25.29   0.00037   3.43
25.32   0.00036   3.44
25.35   0.00035   3.45
25.38   0.00033   3.46
25.41   0.00032   3.47
25.44   0.00031   3.48
25.47   0.00030   3.49
25.50   0.00029   3.50
Descriptive statistics and identifying outliers (1.5 x IQR rule)
Data Lower outliers Upper outliers   Summary statistics
  12                                 Mean                          17
  39                UO               Standard Error       1.488552812
  15                                 Mode                          15
  21
   3 LO                              Minimum                        3
  16                                 Q1                            14
  18                                 Median (Q2)                   16
  20                                 Q3                         19.25
  19                                 Maximum                       39
  13                                 Range = Max - Min             36
  16
  22                                 IQR = Q3 - Q1               5.25
  21                                 1.5 x IQR                  7.875
  14                                 Q1 - 1.5 x IQR             6.125
  15                                 Q3 + 1.5 x IQR            27.125
  18
  14                                 Standard Deviation   6.657010551
  13                                 Sample Variance      44.31578947
  15                                 Kurtosis             6.585835604
  16                                 Skewness             1.558076222
Back to Content
Histogram                                                Back to Content
             Insert the title for the histogram
                   Histogram of the variable

                 Insert the axis label here
                      Horizontal axis label
                       Vertical axis label



            Sample size                         200
            Maximum                              65
            Minimum                              18
            Range = (Maximum -
            Minimum) = 65 - 18
            =                                    47
            Number of classes =                  11 Choose the number of
            k=                                      classes so that you get a
                                                    shape of a histogram that
                                                    would reveal useful
                                                    pattern in data
            Helpful rule is that   YES, this is a
            2^11 (2048) should     possible value
            be >= 200 (sample      for the number of
            size)                  classes for the
                                   sample size of
                                   200
            Approximate class
            width = Range/k =
            47/11 =                    4.272727273
            Class width =                        5 Choose the class width
                                                   so that you get a shape
                                                   of a histogram that would
                                                   reveal useful pattern in
                                                   data
            Actual range for                       YES, with the selected
            classes = class                        class width value you are
            width*k = 5*11 =                       covering the whole range
                                                55 of your data = 47
            Lower limit of the                  15 Choose the lower limit
            first class                            of the first class (should
                                                   be either MIN or a little
                                                   bit smaller than the MIN).
                                                   E.g. if the MIN is 13,
                                                   choose 10 for the lower
                                                   limit of the first class



                   Lower bound        Upper bound         Interval value
   Data                     15                 20          15 up to 20
     21                     20                 25          20 up to 25
     57                     25                 30          25 up to 30
     25                     30                 35          30 up to 35
     38                     35                 40          35 up to 40
     22                     40                 45          40 up to 45
     29                     45                 50          45 up to 50
     18                     50                 55          50 up to 55
     64                     55                 60          55 up to 60
27   60   65   60 up to 65
22   65   70   65 up to 70
39
61
18
22
52
22
18
55
20
42
30
64
63
41
21
63
54
18
26
59
30
64
30
41
23
52
18
32
22
29
25
63
26
31
23
42
28
23
19
37
38
50
26
33
59
32
27
54
63
48
29
38
24
51
25
65
35
35
21
47
62
63
23
59
48
57
19
48
21
40
25
59
57
56
19
54
65
25
30
57
43
44
21
20
49
37
26
62
38
55
24
30
39
59
26
33
20
18
19
61
39
52
20
50
29
55
18
39
35
38
20
60
61
62
21
40
25
50
24
28
22
22
27
54
25
25
30
59
51
38
28
30
43
42
24
47
23
59
22
27
65
27
27
28
22
42
25
41
46
41
29
50
50
34
24
29
35
24
23
31
24
30
22
43
55
38
28
30
35
41
28
65
20
39
19
64
42
24
24
18
36
61
22
55
27
49
29
33
52
26
                            40            38
                                                   Histogram of the variable
                                                  35
                            35

                            30
      Vertical axis label




                            25
                                                                  20
                            20                            17                                      17      17
                                                                          16              15
                            15    13

                            10                                                     8
                                                                                                                  4
                             5

                             0
                                 15 up   20 up   25 up   30 up   35 up   40 up   45 up   50 up   55 up   60 up   65 up
                                 to 20   to 25   to 30   to 35   to 40   to 45   to 50   to 55   to 60   to 65   to 70
                                                                 Horizontal axis label




Frequency
           13
           38
           35
           17
           20
           16
            8
           15
           17
17
 4
Box plot
Instruction:   Insert as much data as you have starting from column A (cell A16).                                              90
               If you have two series only enter your data in columns A and B.
               You don't have to delete data in columns C, D and E.                                                            80
               Replace the default column labels (e.g. Sample1 in A15) with the name
               of your categories (e.g. Female, Male)
               If you have less than 5 box plots simply HIDE columns (H to L)                                                  70
               by right-click the column label and select H ide .




                                                                                         Insert the vertical axis label here
               Insert the chart title here                                                                                     60
               Insert the horizontal axis label here
               Insert the vertical axis label here                                                                             50

     Sample1     Sample2 Sample3 Sample4 Sample5
          67          51      56      54      81                                                                               40
          46          25      19      22      56
          10          52      68      29      31
          47          54      73      26      69                                                                               30
          75          77      28      46      68
          60          53      52      53      60                                                                               20
          31          12      35      74      46
          63          82      71      56      49
          75          57      49      82      62                                                                               10
          47          68      29      43      42
          21          52      55      55      24
          60          53      54      69      52                                                                                0
          46          52      75      20                                                                                            Sample1
          30          33      71      32
          50          43      45
          48          45      65                                                       Sample1     Sample2
          61          58                                                Average           46.8 51.11111111
          45          53                                                Min                 10           12
          21                                                            Q1                32.5         46.5
          33                                                            Median              47         52.5
                                                                        Q3               60.25        56.25
                                                                        Max                 75           82
                                                                        25th Percent      32.5         46.5
                                                                        50th Percent      14.5            6
                                                                        75th Percent     13.25         3.75
                                                                        Min               22.5         34.5
                                                                        Max              14.75        25.75
                                                                          Back to Content


                Insert the chart title here




Sample1           Sample2             Sample3              Sample4   Sample5
                        Insert the horizontal axis label here

          Sample3      Sample4     Sample5
           52.8125 47.21428571 53.33333333
                 19          20          24
               42.5       29.75          45
               54.5        49.5          54
             68.75        55.75        63.5
                 75          82          81
               42.5       29.75          45
                 12       19.75           9
             14.25         6.25         9.5
               23.5        9.75          21
               6.25       26.25        17.5
Box plot with outliers
Instruction:   Insert as much data as you have starting from column A (cell A20).
               If you have two series only enter your data in columns A and B.
               You don't have to delete data in columns C, D and E.
               Replace the default column labels (e.g. Sample1 in A19) with the name
               of your categories (e.g. Female, Male)
               If you have less than 5 box plots simply HIDE columns
               (e.g. if you have one box plot only, hide columns I to L)
               by right-click the column label and select H ide . Some
               additional adjustment of the chart will be required.
               Note: Up to the first five upper/lower outliers are shown.


               Insert the chart title here
               Insert the horizontal axis label here
               Insert the vertical axis label here

    Sample1      Sample2 Sample3 Sample4 Sample5
         67           51      56      54      81
         46           25      19      70      56
         10           52      68      80      31
         47           54      73      26      69
         75           77      60      46      68
         60           53      52      53      60
         31           12      35      74      46
         63           82      71      56      49
         75           57      49      82      62
         47           68      29      43      42
         21           52      55      55      24
         60           53      54      69      52
         46           52      75      60       1
         30           33      71      60     110
         50           43      45       5      37
         48           45      65     120
         61           58       5                                       Descriptive statistics
         45           53     130                                       Min
         21                                                            Q1
        110                                                            Median
        200                                                            Q3
        210                                                            Max
        240                                                            IQR
        190                                                            Number of Upper Outliers
        300                                                            Number of Lower Outliers

                                                                       Upper Outlier
                                                                                              1
                                                                                              2
                                                                                              3
                                                                                              4
                                                                                              5
                                                                       Lower Outlier
                                                                                              1
                                                                                              2
                                                                                              3
                                                                                              4
                                                                                              5
Q2-Q1
Q3-Q2
For the Whiskers
Q3+1.5*IQR
Q1-1.5*IQR
Upper Whisker
Lower Whisker
Wupper-Q3
Q1-Wlower
For the Outliers
First
Max
Min
Second
Max
Min
Third
Max
Min
Fourth
Max
Min
Fifth
Max
Min
                                        350
                                                          Insert the chart title here
                                        300
  Insert the vertical axis label here




                                        250



                                        200



                                        150



                                        100



                                         50



                                          0
                                               Sample1          Sample2            Sample3              Sample4   Sample5
                                                                     Insert the horizontal axis label here
                                                                    * Lower outlier * Upper outlier



Sample1                                       Sample2 Sample3       Sample4         Sample5
     10                                            12       5             5               1
     46                                          46.5      46         51.25            39.5
     60                                          52.5    55.5            58              52
     75                                         56.25   70.25            71              65
    300                                            82     130           120             110
     29                                          9.75   24.25         19.75            25.5
      5                                             2       1             1               1
      0                                             2       1             1               1


                                        300        82     130             120             110
                                        240        77
                                        210
                                        200
                                        190

                                                   12       5                5               1
                                                   25
   14          6         9.5      6.75         12.5
   15       3.75       14.75        13          13

 118.5    70.875     106.625   100.625       103.25
   2.5    31.875       9.625    21.625         1.25
  110         68          75        82           81
   10         33          19        26           24
   35      11.75        4.75        11           16
   36       13.5          27     25.25         15.5


   300          82      130           120          110
#N/A            12        5             5            1

   240          77   #N/A      #N/A         #N/A
#N/A            25   #N/A      #N/A         #N/A

   210   #N/A        #N/A      #N/A         #N/A
#N/A     #N/A        #N/A      #N/A         #N/A

   200   #N/A        #N/A      #N/A         #N/A
#N/A     #N/A        #N/A      #N/A         #N/A

   190   #N/A        #N/A      #N/A         #N/A
#N/A     #N/A        #N/A      #N/A         #N/A
          Back to Content




Sample5
Stem and leaf plot

Instruction      Delete the sample data below and enter your data in column starting from cell A6.

    Data
            56
            22
            47
            55
            66
            57
            32
            37
            40              Min            9               Stem           Leaf                       Example
            40              Max         101                      0   9
            62              N            27                      1                            Data
            77              Leaf unit    10                      2   2                           5
            36                                                   3   236777                      9
            97                                                   4   00577899                   45
            37                                                   5   5567                       31
            70                                                   6   26                          4
            96                                                   7   07                         19
            45                                                   8                              62
            48                                                   9   67                         41
            47                                                  10   1                          23
            37                                                                                  28
            33                                                                                  33
            55                                                                                  26
            49                                                                                  21
            49                                                                                  24
             9                                                                                  15
           101                                                                                  14
                                                                                                22
                                                                                                22
                                                                                                24
                                                                                                25
                   Back to Content




  Example
Min  4      Stem      Leaf
Max 62         0   459
N   20         1   459
               2   122344568
               3   13
               4   15
               5
               6   2
Stem and leaf plot

Instruction        Delete the sample data below and enter your data in column starting from cell A6.

    Data
               1
              10
               1
              10
               1
               1
              10
               5              Min           1               Stem              Leaf                            Exam
               1              Max         10                      1   0000000000000000
               1              N           60                      2   0000                             Data
               8              Leaf unit    1                      3   0                                   5
               1                                                  4   0                                   9
              10                                                  5   00000                              45
               2                                                  6   000                                31
               1                                                  7   0                                   4
               9                                                  8   000000                             19
               5                                                  9   00000                              62
               2                                                 10   000000000000000000                 41
               1                                                                                         23
               8                                                                                         28
              10                                                                                         33
               5                                                                                         26
               9                                                                                         21
              10                                                                                         24
              10                                                                                         15
               9                                                                                         14
               6                                                                                         22
              10                                                                                         22
               1                                                                                         24
               5                                                                                         25
               1
               9
               2
               1
               7
              10
               9
               5
              10
              10
              10
               1
               8
               1
               6
              10
               1
               6
              10
              10
 8
10
 3
10
 8
 1
 8
10
 4
 2
                   Back to Content




  Example
Min  4      Stem      Leaf
Max 62         0   459
N   20         1   348
               2   237
               3   126
               4   015
               5   049
               6   389
Splitting the Stem and leaf plot

Instruction      Delete the sample data below and enter your data in column starting from cell A6.

    Data
            50
            81
            40
            41
            77
            47
            37
            13
            45              Min     13               Stem            Leaf                             Example
            35              Max 105                        0
            63              N    51                        0                                   Data
            60                                             1   344                               55
            82                                             1                                     58
            73                                             2   01134                             54
            93                                             2   6                                 65
            95                                             3   1224                              66
            54                                             3   5777                              61
            66                                             4   01                                69
            24                                             4   578                               67
            20                                             5   034                               76
            85                                             5                                     58
            34                                             6   0223                              54
            99                                             6   69                                75
            26                                             7   344                               73
            62                                             7   7                                 70
            89                                             8   1124                              59
            95                                             8   589                               60
            21                                             9   03                                64
            97                                             9   55579                             62
           105                                            10   1                                 60
            88                                            10   5                                 61
            53
            48
            74
            31
            62
            37
            23
            14
            74
            81
            69
            84
            32
            32
            95
            37
            90
            14
 21
101
                  Back to Content




 Example
Min 54     Stem    Leaf
Max 76        5   44
N   20        5   5889
              6   001124
              6   5679
              7   03
              7   56
Back-to-back stem and leaf plot
Instruction Delete the sample data below (yellow area) and enter your data in columns C and D starting from cells C8 and D8 res
            Data1 (cell C7) and Data2 (cell D7) with your own. Insert the leaf unit for each variable (cells E19 and F19). Insert the
            to keep from original number (cell I21) and number (cell I22) you need to use to multiply original data to get an integer

                           Data1      Data2
         89         79       8.882       7.94
         60         83            6     8.292
         75         46        7.47      4.643
         55         75       5.528       7.47
         76         76       7.571      7.585
         47         77          4.7      7.65
         82         24       8.167      2.412
         78         88       7.822      8.833                           Data1        Data2
         76         72       7.598      7.167              Min            3.408          0.53
         62         40       6.231           4             Max             10.7         10.76
         64         76       6.419      7.643              N                 31            47
        107         18        10.7       1.76              Leaf unit         10            10
         96         96       9.571      9.648
         90        106       8.998      10.58              Rounded to decimal places                    1
         83         94       8.333      9.429              Multiply with to get an integer             10
         93         80       9.333           8
        101         96       10.14      9.585
        100         82       9.999      8.175
         34         80       3.408           8
         73         95       7.295         9.5
         89         92       8.938      9.167
         79        108       7.882      10.76
         52         98       5.237      9.763
         73         94       7.333       9.41
         87         92       8.714      9.167
         78         93       7.833      9.348
         80         82       7.998      8.167
         59         36       5.936      3.647
         90         39            9     3.936
         95         72          9.5     7.167
         61         76       6.057      7.647
                     5                   0.53
                    62                  6.173
                    73                  7.295
                    84                  8.353
                    51                  5.062
                    82                  8.175
                    82                  8.235
                    76                  7.588
                    76                  7.647
                    78                  7.825
                    92                  9.167
                    80                  7.996
                    49                  4.885
                    38                   3.82
                    61                  6.057
                    69                  6.938
                                                      Back to Content

 ns C and D starting from cells C8 and D8 respectively. Replace the default names
r each variable (cells E19 and F19). Insert the number of decimal places you want
  use to multiply original data to get an integer.




                                   Data1      S      Data2
                                              0   5
                                              1   8
                                              2   4
                                         4    3   689
                                         7    4   069
                                       952    5   1
                                      4210    6   129
                                  98866533    7   223566666789
                                    997320    8   0002222348
                                     65300    9   2223445668
                                       710   10   68
Normal quantile plot
   Data Rank   Proportion z-score
     12       2 0.0802469 -1.4034                        Normal quantile plot
     39      20 0.9691358 1.8682
     15       9 0.4259259 -0.1868
     21      18 0.8703704 1.1281
      3       1 0.0308642 -1.8682
     16      12 0.5740741 0.1868
     18      14 0.6728395 0.4478
     20      16 0.7716049 0.7441
     19      15 0.7222222 0.5895
     13       4 0.1790123 -0.9191




                                    Data
     16      12 0.5740741 0.1868
     22      19 0.9197531 1.4034
     21      18 0.8703704 1.1281
     14       6 0.2777778 -0.5895
     15       9 0.4259259 -0.1868
     18      14 0.6728395 0.4478
     14       6 0.2777778 -0.5895
     13       4 0.1790123 -0.9191
     15       9 0.4259259 -0.1868
     16      12 0.5740741 0.1868     -2.5   -2   -1.5   -1   -0.5
                                             Back to Content


Normal quantile plot
           45

           40

           35

           30

           25

           20

           15

           10

            5

            0
    0.5         0        0.5   1   1.5   2         2.5
          Normal score
Regression analysis                Regression Statistics              Back to Content
   Name of         Name of
Explanatory var. Response var.   Correlation      0.964488347   Insert the var. names here
                                                                                                                                           Insert the title he
             100            76   R^2              0.930237772   Name of Explanatory var.                                 90
              55            45   Standard Error   4.796712924   Name of Response var.                                    80
              34            31   Sample size               10
                                                                                                                         70
              67            55   Intercept (b0)   1.695649964   Insert the titles here




                                                                                                   Vertical axis label
              52            42   Slope (b1)       0.789714402   Insert the title here                                    60
              66            48                                  Residual plot                                            50
              35            31                                  Normal quantile plot                                     40
              87            80
                                                                                                                         30
              70            59                                  Insert the axis labels here
              52            38                                  Horizontal axis label                                    20
                                                                Vertical axis label                                      10
                                                                                                                          0
                                                                Name of the explanatory var.
                                                                                                                              0       20
                                                                Residuals

                                                                Normal score

                                     Regression model
                                                                                                                         12
                                   Name of                                Name of
                                 Response var. 1.695649964 + 0.789714402 Explanatory                                     10
                                      =                                      var.                                         8
                                                                                                                          6
                                   Name of         Name of
                                                                                                      4




                                                                                                   Residuals
                                  Explanatory     Response       Estimate         Residual     Rank Proportion z-score
                                      var.           var.                                             2
                                           100             76   80.66709015 -4.66709015           3                       0
                                                                                                                         0.2560976   -0.6554
                                            55             45   45.12994207 -0.12994207           5                      -2 0
                                                                                                                         0.4512195     20
                                                                                                                                     -0.1226
                                            34             31   28.54593963 2.454060372           9                      0.8414634   1.00049
                                                                                                                         -4
                                            67             55   54.60651489  0.39348511           6                      0.5487805   0.12258
                                            52             42   42.76079886 -0.76079886           4                      -6
                                                                                                                         0.3536585   -0.3755
                                            66             48   53.81680049 -5.81680049           1                      -8
                                                                                                                         0.0609756   -1.5466
                                            35             31   29.33565403  1.66434597           7                      0.6463415   0.37546
                                            87             80   70.40080293 9.599197073          10                      0.9390244   1.54664
                                            70             59    56.9756581 2.024341905           8                      0.7439024   0.65542
                                                                                                                                           Normal quantile p
52   38   42.76079886   -4.76079886   2                          0.1585366        Normal quantile p
                                                                              -1.0005




                                      Name of Explanatory var.
                                                        -2             -1.5      -1
Insert the title here



                                      y = 0.7897x + 1.6956
                                           R² = 0.9302




    40            60             80           100            120
         Horizontal axis label



   Residual plot




    40            60             80           100            120




   Name of the explanatory var.



Normal quantile plot
Normal quantile plot
            12

            10

             8

             6

             4

             2

             0
    -0.5          0       0.5   1   1.5   2
             -2

             -4

             -6

             -8
           Normal score
Calculate the mean and standard deviation of a random variable

   x(i)       p(i)          xp         x-mu      (x-mu)^2    (x-mu)^2*p
          0           0.1          0      -1.7        2.89        0.289
          1           0.3        0.3      -0.7        0.49        0.147
          2           0.4        0.8       0.3        0.09        0.036
          3           0.2        0.6       1.3        1.69        0.338




                       1         1.7      -0.8        5.16         0.81


Mean (mu)             1.7
Variance             0.81
Sigma                 0.9
Back to Content
Binomial distribution                                                   Back to Content

Probability                                              0.5
                                                                                                           0.1
Sample size                                               80
Number of successes (k*)                                  40                                              0.09
Mean                                                      40                                              0.08
Variance                                                  20                                              0.07
Standard deviation                              4.472135955                                               0.06




                                                                                               P(X = k)
z* value                                                   0
                                                                                                          0.05
Normal approximation     OK to use it
                                                                                                          0.04
                                                                                                          0.03
                                                                                                          0.02
                            Exact binomial distribution Normal approximation
                                                                                                          0.01
         P(k=k*)                             0.088927879
         P(k<=k*)                            0.544463939                    0.5
         P(k>k*)                             0.455536061                    0.5


Note : The graph illustrates the Normal approximation of the binomial distribution.




                                           k                           P(X=k)             z-score


                                            0                              8.27181E-25    -8.94427
                                            1                              6.61744E-23    -8.72067
                                            2                              2.61389E-21    -8.49706
                                            3                              6.79612E-20    -8.27345
                                            4                              1.30825E-18    -8.04984
                                            5                              1.98854E-17    -7.82624
                                            6                              2.48568E-16    -7.60263
                                            7                              2.62772E-15    -7.37902
                                            8                              2.39779E-14    -7.15542
                                            9                              1.91823E-13    -6.93181
                                           10                              1.36195E-12     -6.7082
                                           11                              8.66693E-12     -6.4846
                                           12                              4.98349E-11    -6.26099
                                           13                              2.60675E-10    -6.03738
                                           14                              1.24751E-09    -5.81378
                                           15                              5.48906E-09    -5.59017
                                           16                              2.22993E-08    -5.36656
                                           17                              8.39504E-08    -5.14296
                                           18                              2.93826E-07    -4.91935
                                           19                              9.58802E-07    -4.69574
                                           20                              2.92434E-06    -4.47214
                                           21                              8.35527E-06    -4.24853
                                           22                              2.24073E-05    -4.02492
                                           23                              5.65054E-05    -3.80132
                                           24                                 0.0001342   -3.57771
                                           25                              0.000300609     -3.3541
26   0.000635903      -3.1305
27   0.001271806    -2.90689
28   0.002407348    -2.68328
29   0.004316624    -2.45967
30    0.00733826    -2.23607
31   0.011835904    -2.01246
32   0.018123728    -1.78885
33   0.026361786    -1.56525
34   0.036441293    -1.34164
35    0.04789427    -1.11803
36   0.059867838    -0.89443
37   0.071194185    -0.67082
38   0.080561841    -0.44721
39   0.086758906    -0.22361
40   0.088927879            0
41   0.086758906    0.223607
42   0.080561841    0.447214
43   0.071194185     0.67082
44   0.059867838    0.894427
45    0.04789427    1.118034
46   0.036441293    1.341641
47   0.026361786    1.565248
48   0.018123728    1.788854
49   0.011835904    2.012461
50    0.00733826    2.236068
51   0.004316624    2.459675
52   0.002407348    2.683282
53   0.001271806    2.906888
54   0.000635903    3.130495
55   0.000300609    3.354102
56      0.0001342   3.577709
57   5.65054E-05    3.801316
58   2.24073E-05    4.024922
59   8.35527E-06    4.248529
60   2.92434E-06    4.472136
61   9.58802E-07    4.695743
62   2.93826E-07     4.91935
63   8.39504E-08    5.142956
64   2.22993E-08    5.366563
65   5.48906E-09     5.59017
66   1.24751E-09    5.813777
67   2.60675E-10    6.037384
68   4.98349E-11     6.26099
69   8.66693E-12    6.484597
70   1.36195E-12    6.708204
71   1.91823E-13    6.931811
72   2.39779E-14    7.155418
73   2.62772E-15    7.379024
74   2.48568E-16    7.602631
75   1.98854E-17    7.826238
76   1.30825E-18    8.049845
77   6.79612E-20    8.273452
78   2.61389E-21    8.497058
79   6.61744E-23    8.720665
80   8.27181E-25    8.944272
        Binomial probability distribution
 0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
   0
       0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78
                                             k

                          P(X=k)         Normal approximation




  Cumulative
                          Normal
    normal
                       approximation
 approximation
       1.52973E-17
       1.01189E-16             1.53E-17
       6.37134E-16         8.58915E-17
       3.81879E-15         5.35946E-16
       2.17889E-14         3.18166E-15
       1.18352E-13         1.79701E-14
       6.12019E-13         9.65628E-14
       3.01319E-12         4.93667E-13
       1.41248E-11         2.40117E-12
       6.30463E-11         1.11117E-11
       2.67968E-10         4.89215E-11
       1.08463E-09         2.04922E-10
       4.18109E-09         8.16663E-10
       1.53512E-08         3.09646E-09
       5.36881E-08         1.11701E-08
       1.78871E-07         3.83369E-08
       5.67778E-07         1.25183E-07
       1.71729E-06         3.88907E-07
       4.94992E-06         1.14952E-06
       1.35989E-05         3.23263E-06
       3.56155E-05         8.64902E-06
       8.89373E-05         2.20166E-05
       0.000211803         5.33218E-05
       0.000481163         0.000122866
       0.001042993         0.000269359
       0.002157934          0.00056183
0.004263029    0.00111494
0.008044543   0.002105095
 0.01450754   0.003781514
0.025016908   0.006462997
0.041275908   0.010509367
0.065208291       0.016259
0.098724358   0.023932383
0.143381953   0.033516067
0.199994526   0.044657595
0.268276467   0.056612573
0.346632836   0.068281941
0.432182497   0.078356369
0.521048953   0.085549661
0.608876961   0.088866456
0.691462461   0.087828008
0.765346417      0.0825855
0.828235026   0.073883955
0.879164511   0.062888609
0.918405679   0.050929485
0.947172364   0.039241168
0.967236145   0.028766684
 0.98055021   0.020063781
0.988956093   0.013314065
0.994005385   0.008405883
0.996891091   0.005049293
 0.99846018   0.002885706
 0.99927192   0.001569089
 0.99967146    0.00081174
0.999858561    0.00039954
0.999941922   0.000187101
0.999977259   8.33614E-05
0.999991511   3.53367E-05
0.999996979   1.42515E-05
0.999998975   5.46847E-06
0.999999669   1.99638E-06
0.999999898   6.93411E-07
 0.99999997   2.29144E-07
0.999999992   7.20439E-08
0.999999998   2.15504E-08
0.999999999   6.13313E-09
          1   1.66065E-09
          1   4.27801E-10
          1   1.04851E-10
          1   2.44496E-11
          1   5.42422E-12
          1   1.14497E-12
          1   2.29927E-13
          1   4.38538E-14
          1   7.99361E-15
          1   1.44329E-15
          1   2.22045E-16
          1              0
          1              0
          1              0
          1              0
Inference for a single proportion                                      Back to Content


Instruction:                                     Enter the sample counts, sample size,
                                                 the hypothesised proportion, confidence
                                                 level and given marking of error
                                                 in the yellow cells.


Sample count (the number of success) X =                       13
Sample size                           ����=                      20
Hypothesised population proportion   ����_0=                    0.5

Conditions for use of z -distribution
Conditions fulfilled

             z -test: one proportion - inference for proportion

Sample proportion                                            0.65

Standard error                                           0.11180


Test statistic                                               1.34

P -value, i.e. 2P (Z >=|z |)                          0.17971249

P -value, i.e. P (Z <=z ) or P (Z >=z )               0.08985625


            Confidence interval for the population proportion

Confidence Level                                             95%

           Large-sample confidence interval for a single proportion

Standard error                                      0.106653645

The z critical value for 95% confidence is          1.959963985

Margin of error                                     0.209037303

Approximate level 95% confidence interval
Lower bound                                         0.440962697
Upper bound                                         0.859037303

          The Plus Four confidence interval for a single proportion

Estimation of population proportion                        0.625

Standard error                                      0.098821177

Margin of error                                     0.193685948

Approximate level 95% confidence interval
Lower bound                                         0.431314052
Upper bound                                         0.818685948

                 Sample size required for a given margin of error

Given margin of error                                         5%

Sample size required                                         384
Inference for two proportions                                            Back to Content


Instruction:                                       Enter the counts, sample sizes and
                                                   confidence level




First sample: count of successes                                1392
First sample: sample size                                       5348

Second sample: count of successes                               1748
Second sample: sample size                                      8471


Conditions for use of z-distribution
Conditions fulfilled

     z -test: two populations - inference for two proportions

First sample proportion                                 0.260284218
Second sample proportion                                 0.20635108

Pooled proportion                                             0.2272


Pooled standard error                                        0.00732


Test statistic                                                   7.37

P -value, i.e. 2P (Z >=|z |)                             1.71418E-13

P -value, i.e. P (Z <=z ) or P (Z >=z )               0.00000000000

         Confidence interval for the population proportion

Confidence Level                                                 95%

  Large-sample confidence interval for compering two proportions

Difference in sample proportions                        0.053933138

Standard error                                          0.007438724

The z critical value for 95% confidence is              1.959963985

Margin of error for confidence level 95%                0.014579631

Approximate level 95% confidence interval
Lower bound                                             0.039353507
Upper bound                                             0.068512769

  The Plus Four confidence interval for a difference in proportions

The plus four estimate (first sample)                   0.260373832
The plus four estimate (second sample)                  0.206420394

Difference in sample proportions                        0.053953438

Standard deviation of difference                        0.007438981

Margin of error for confidence level 95%                0.014580135

Approximate level 95% confidence interval
Lower bound                                             0.039373303
Upper bound                                             0.068533572
The one sample t-test for mean
Data
    -8.36         t-test: One sample - inference for the Mean of a population
     1.63
    -2.27   Hypothesised Mean Value
    -2.93
     -2.7   Mean
    -2.93   Variance
    -9.14   Standard Deviation
    -2.64   Sample size
     6.82   Degree of Freedom
    -2.35
    -3.58   t Statistic
     6.13
        7    ����_0:����=����_0                  ����_0:����≠����_0
   -15.25
    -8.66   P -value; i.e. 2P (T >=|t |)
    -1.03
    -9.16    ����_0:����=����_0                  ����_0:����≤����_0   ����_0:����>����_0
    -1.25
    -1.22   P -value; i.e. P (T <=t ) or P(T >=t )
   -10.27
    -5.11
     -0.8                 Confidence interval for the mean of a population
    -1.44
     1.28   Confidence Level
    -0.65
     4.34   Margin of error
    12.22
    -7.21   Lower bound
    -0.09   Upper bound
     7.34
     5.04
    -7.24
    -2.14
    -1.01
    -1.41
    12.03
    -2.56
     4.33
     2.35
                    Back to Content


Mean of a population

                         0.95

                    -1.09974
                    35.89074
                    5.990888
                          39
                          38

                    -2.13669



                    0.039123



                    0.019561


n of a population

                        95%

                    1.942021

                    -3.04176
                    0.842278
The two sample t-test for means
Sample1 Sample2
      24      42
      56      46
      43      43
      59      10
      58      55
      52      17
      71      26
      62      60
      43      62
      54      53
      49      37
      57      42
      61      33
      33      37
      44      41
      46      42
      67      19
      43      55
      49      54
      57      28
      53      20
              48
              85
wo sample t-test for means                                                                        Back to Content

                                      t-test: Two sample - comparing two means

                                                                              Sample1            Sample2
             Mean                                                                51.47619048      41.52173913
             Variance                                                            121.1619048      294.0790514
             Standard Deviation                                                  11.00735685      17.14873323
             Sample size                                                                  21               23
             Sample size - 1                                                              20               22
             Degree of Freedom (smaller of n1-1 and n2-1)                                 20
             Software approximation for the degree of freedom                    37.85540066

             t Statistic                                                          2.310889198

             Two-sided alternative hypothesis
             P -value; i.e. 2P (T >=|t |) conservative approach                   0.031624904
             Using software approximation for the degree of freedom               0.026514927

             One-sided alternative hypothesis
             P -value; i.e. P (T <=t ) or P(T >=t ) conservative approach         0.015812452
             Using software approximation for the degree of freedom               0.013257463


                           The two-sample t confidence interval

             Confidence Level                                                            95%

             Margin of error based on conservative approach                       8.985554852
             Lower bound                                                          0.968896493
             Upper bound                                                           18.9400062

             Margin of error based on the software approximation for the df       8.728083678
             Lower bound                                                          1.226367667
             Upper bound                                                          18.68253502

                                   The pooled two-sample t procedures

             Pooled variance                                                       211.737553
             Pooled sample t statistic                                               2.2665516
             Degree of freedom                                                              42
             P -value; i.e. 2P (T >=|t |) conservative approach                   0.028629483
             P -value; i.e. P (T <=t ) or P(T >=t ) conservative approach         0.014314741

             Margin of error based on conservative approach                       8.863198229
             Lower bound                                                          1.091253117
             Upper bound                                                          18.81764957
The matched pairs t test

Sample1    Sample2     Difference
      3.33       0.27          3.06
      3.67       0.59          3.08
      2.67       0.32          2.35
      3.33       0.19          3.14
      3.33       1.26          2.07
      3.67       0.11          3.56
      4.67         0.3         4.37
      2.67         0.4         2.27
         6       1.59          4.41
      4.33         0.6         3.73
      3.33       0.65          2.68
      0.67       0.69         -0.02
      1.33       1.26          0.07
      0.33       0.23           0.1
         2       0.38          1.62
                                                                                      Back to Content

                                        Matched pairs t -test

                                                       Sample1         Sample2        Difference
Mean                                                           3.022    0.589333333    2.4326667
Variance                                                2.246317143     0.197935238    2.1325352
Standard Deviation                                      1.498771878     0.444899132    1.4603203
Correlation                                                                            0.2337403
Sample size                                                                                   15
Degree of freedom                                                                             14

Hypothesised Mean Difference Value                                0

t Statistic                                             6.451788554

Two-sided alternative hypthesis
P -value; i.e. 2P (T >=|t |)                             1.51815E-05

One-sided alternative hypothesis
P -value; i.e. P(T <=t ) or P(T >=t )                    7.59076E-06

                         The matched pairs t confidence interval

Confidence Level                                                95%

Margin of error                                         0.808698398
Lower bound                                             1.623968269
Upper bound                                             3.241365064
Two-way tables and chi-square tests

Instruction         Insert your two-way table into the same size two-way table highlighted in yellow below.
                    Insert the significance level in the highlighted cell in yellow on the right (usual values are 5%, 1% or 10%).
                    Validation of the chi-square test is given below the significance level (Adequate/Not adequate)
                    Important: If you are pasting data from the Two-way (raw) worksheet make sure that all the empty cells are
                                 filled with zeros after you pasted them below.

2x2                                                                   Expected
      150      55       205                                             117.95        87.05        205
       60     100       160                                              92.05        67.95        160
      210     155       365                                               210          155         365



2x3                                                                   Expected
      150      55        45      250                                    112.90        83.33      53.76
       60     100        55      215                                     97.10        71.67      46.24
      210     155       100      465                                      210          155        100



2x4                                                                   Expected
      150      55        45        50      300                          115.60        85.32      55.05
       60     100        55        30      245                           94.40        69.68      44.95
      210     155       100        80      545                            210          155        100



2x5                                                                   Expected
      150      55        45        50        5      305                 107.65        79.45      51.26
       60     100        55        30       45      290                 102.35        75.55      48.74
      210     155       100        80       50      595                   210          155        100



2x6                                                                   Expected
      150      55        45        50        5        10      315       108.44        80.04      51.64
       60     100        55        30       45         5      295       101.56        74.96      48.36
      210     155       100        80       50        15      610         210          155        100



3x3                                                                   Expected
       30      39        30       99                                     34.22        30.56      34.22
       11       1        19       31                                     10.72         9.57      10.72
       43      35        35      113                                     39.06        34.88      39.06
       84      75        84      243                                        84           75         84


3x4                                                                   Expected
      150      55        45         5      255                          107.88        78.46      53.94
       60     100        55        10      225                           95.19        69.23      47.60
       10       5        10        15       40                           16.92        12.31       8.46
      220     160       110        30      520                            220          160        110
3x5                                             Expected
      150    55    45     5    10   265           106.97   77.80   53.49
       60   100    55    10    10   235            94.86   68.99   47.43
       10     5    10    15     5    45            18.17   13.21    9.08
      220   160   110    30    25   545             220     160     110


3x6                                             Expected
      150    55    45     5    10    50   315     104.21   75.79   52.11
       60   100    55    10    10    30   265      87.67   63.76   43.83
       10     5    10    15     5    40    85      28.12   20.45   14.06
      220   160   110    30    25   120   665       220     160     110


4x4                                             Expected
      150    55    45     5   255                 105.92   74.54   58.85
       60   100    55    10   225                  93.46   65.77   51.92
       10     5    10    15    40                  16.62   11.69    9.23
       50    30    40    10   130                  54.00   38.00   30.00
      270   190   150    40   650                   270     190     150

4x5                                             Expected
      150    55    45     5    15   270           105.65   74.35   58.70
       60   100    55    10     5   230            90.00   63.33   50.00
       10     5    10    15     5    45            17.61   12.39    9.78
       50    30    40    10    15   145            56.74   39.93   31.52
      270   190   150    40    40   690             270     190     150

4x6                                             Expected
      150    55    45     5    15     0   270      93.46   65.77   51.92
       60   100    55    10     5    50   280      96.92   68.21   53.85
       10     5    10    15     5    30    75      25.96   18.27   14.42
       50    30    40    10    15    10   155      53.65   37.76   29.81
      270   190   150    40    40    90   780       270     190     150

5x5                                             Expected
      150    55    45     5    15   270            92.87   82.55   61.91
       60   100    55    10     5   230            79.11   70.32   52.74
       10     5    10    15     5    45            15.48   13.76   10.32
       50    30    40    10    15   145            49.87   44.33   33.25
        0    50    30    10     5    95            32.68   29.04   21.78
      270   240   180    50    45   785             270     240     180

5x6                                             Expected
      150    55    45     5    15    10   280      90.54   80.48   60.36
       60   100    55    10     5    10   240      77.60   68.98   51.74
       10     5    10    15     5    10    55      17.78   15.81   11.86
       50    30    40    10    15    10   155      50.12   44.55   33.41
        0    50    30    10     5    10   105      33.95   30.18   22.63
      270   240   180    50    45    50   835       270     240     180

6x6                                             Expected
      150    55    45     5    15    10   280      83.28   73.23   53.13
       60   100    55    10     5    10   240      71.38   62.77   45.54
       10     5    10    15     5    10    55      16.36   14.38   10.44
       50    30    40    10    15    10   155      46.10   40.54   29.41
        0    50    30    10     5    10   105      31.23   27.46   19.92
       20    15     5    60    35     5   140      41.64   36.62   26.56
      290   255   185   110    80    55   975       290     255     185
                                                                 Back to Content


ghlighted in yellow below.
n the right (usual values are 5%, 1% or 10%).
ce level (Adequate/Not adequate)
worksheet make sure that all the empty cells are


                                                             Significance level                5%
                                                             Chi-square approximation Adequate
                                                             Chi-square                46.79934247
                                                             Degree of freedom                   1
                                                             P -value                  7.86398E-12
                                                             Critical value            3.841458821

                                                             Significance level                5%
                             250                             Chi-square approximation Adequate
                             215                             Chi-square                50.28642857
                             465                             Degree of freedom                   2
                                                             P -value                  1.20349E-11
                                                             Critical value            5.991464547

                                                             Significance level                5%
                        44.04       300                      Chi-square approximation Adequate
                        35.96       245                      Chi-square                52.62139957
                           80       545                      Degree of freedom                   3
                                                             P -value                   2.2078E-11
                                                             Critical value            7.814727903

                                                             Significance level                5%
                        41.01      25.63        305          Chi-square approximation Adequate
                        38.99      24.37        290          Chi-square                89.31455716
                           80         50        595          Degree of freedom                   4
                                                             P -value                   1.8412E-18
                                                             Critical value            9.487729037

                                                             Significance level                5%
                        41.31      25.82        7.75   315   Chi-square approximation Adequate
                        38.69      24.18        7.25   295   Chi-square                90.74442209
                           80         50          15   610   Degree of freedom                   5
                                                             P -value                  4.68732E-18
                                                             Critical value            11.07049769

                                                             Significance level                5%
                              99                             Chi-square approximation Adequate
                              31                             Chi-square                18.27921151
                             113                             Degree of freedom                   4
                             243                             P -value                   0.00108828
                                                             Critical value            9.487729037

                                                             Significance level                5%
                        14.71       255                      Chi-square approximation Adequate
                        12.98       225                      Chi-square                137.1299329
                         2.31        40                      Degree of freedom                   6
                           30       520                      P -value                  4.04068E-27
                                                             Critical value            12.59158724
                              Significance level                5%
14.59   12.16    265          Chi-square approximation Adequate
12.94   10.78    235          Chi-square                137.0497627
 2.48    2.06     45          Degree of freedom                   8
   30      25    545          P -value                  9.74011E-26
                              Critical value            15.50731306

                              Significance level                5%
14.21   11.84   56.84   315   Chi-square approximation Adequate
11.95    9.96   47.82   265   Chi-square                170.7114999
 3.83    3.20   15.34    85   Degree of freedom                  10
   30      25    120    665   P -value                  1.97596E-31
                              Critical value            18.30703805

                              Significance level                5%
15.69    255                  Chi-square approximation Adequate
13.85    225                  Chi-square                141.2631615
 2.46     40                  Degree of freedom                   9
 8.00    130                  P -value                  5.65837E-26
   40    650                  Critical value             16.9189776

                              Significance level                5%
15.65   15.65    270          Chi-square approximation Adequate
13.33   13.33    230          Chi-square                151.6687196
 2.61    2.61     45          Degree of freedom                  12
 8.41    8.41    145          P -value                   2.5996E-26
   40      40    690          Critical value            21.02606982

                              Significance level                5%
13.85   13.85   31.15   270   Chi-square approximation Adequate
14.36   14.36   32.31   280   Chi-square                 241.556242
 3.85    3.85    8.65    75   Degree of freedom                  15
 7.95    7.95   17.88   155   P -value                   6.7816E-43
   40      40      90   780   Critical value            24.99579014

                              Significance level                5%
17.20   15.48    270          Chi-square approximation Adequate
14.65   13.18    230          Chi-square                207.5428337
 2.87    2.58     45          Degree of freedom                  16
 9.24    8.31    145          P -value                  2.35925E-35
 6.05    5.45     95          Critical value             26.2962276
   50      45    785

                              Significance level                5%
16.77   15.09   16.77   280   Chi-square approximation Adequate
14.37   12.93   14.37   240   Chi-square                220.7204152
 3.29    2.96    3.29    55   Degree of freedom                  20
 9.28    8.35    9.28   155   P -value                  8.57616E-36
 6.29    5.66    6.29   105   Critical value            31.41043284
   50      45      50   835

                              Significance level                5%
31.59   22.97   15.79   280   Chi-square approximation Adequate
27.08   19.69   13.54   240   Chi-square                456.0260102
 6.21    4.51    3.10    55   Degree of freedom                  25
17.49   12.72    8.74   155   P -value                  9.50369E-81
11.85    8.62    5.92   105   Critical value            37.65248413
15.79   11.49    7.90   140
 110       80      55   975
Two-way table (pivot table)
Instruction:   Enter your first categorical variable (with smaller number of categories, up to 6 categories) in column A starting
               Enter your second categorical variable (with larger number of categories, up to 6 categories) in column B startin
               If the pivot table does not display, insert a new pivot table by putting the variable with smaller number of catego
               into the rows and the other categorical variable into the column of your pivot table. Any of these two variables
               could be put into the Data section on the pivot table layout.
               Click anywhere in the pivot table to bring the PivotTable Field List window on the screen
               Click the PivotTable Tools tab and then Options
               Click Refresh > Refresh All (alternatively press Ctrl + Alt + F5) and your table will be complete.
               Make sure that the (blank) category is NOT included, i.e. that it is filtered out from the pivot table.
                              To complete a chi-square test
               Copy the two-way table. Switch to the Two-way worksheet
               Paste your data into an appropriate two-way table
               (for the example below, that would be 2 x 4 table)

Catvar1        Catvar2
M              WD                       Count of Catvar1 Column Labels
M              TF                       Row Labels                               F P TF WD (blank)
F              P                        F                                        1 3
F              P                        M                                          2 2   2
M              P                        (blank)
F              F                        Grand Total                              1 5    2    2
M              WD
M              TF
M              P
F              P
                                  Back to Content

o 6 categories) in column A starting from cell A18
p to 6 categories) in column B starting from cell B18
 able with smaller number of categories
t table. Any of these two variables

on the screen

le will be complete.
ut from the pivot table.




             Grand Total
                        4
                        6

                           10

				
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posted:11/9/2012
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