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Descriptive statistics

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Descriptive statistics

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									                        ASSIGNMENT NO.1


 Question No.1:

      The following data shows the marks of the students in a statistic class.
Calculate all descriptive statistics.

9.0    10.2   11.3   12.1   10.7   13.8   10.8
11.6   13.6   16.4   11.0   15.8   9.3    13.7
11.7   11.0   8.0    12.0   11.5   9.7    11.6
10.1   14.1   10.0   9.9    13.4   15.7   11.5
12.3   9.8    13.0   9.1    8.3    12.9   14.0
10.5   13.2   10.5   10.6   12.5   15.1   12.8
10.4   11.2   9.3    11.7   17.7   13.9   16.9
13.4   11.8   16.8   14.2   11.8   9.6    11.9
8.7    14.7   10.9   17.9   11.5   14.7   15.9
11.8   10.6   12.6   12.6   15.7   14.7   9.9

Solution:

Procedure:
         Firstly we open Minitab software then we type all the observations
in worksheet of Minitab in a column. Then we go to Menu bar and click on
stat then to basic statistics and in basic statistics we select the option
Display Descriptive statistics. It shows us the results of descriptive
statistics.

Output:
              Total
              Count N N* CumN CumPct Mean SE Mean TrMean
               70   70 0 70    100   12.244 0.281  12.158

              StDev Variance CoefVar Sum sum of squares Minimum
              2.352 5.530 19.21 857.100 10876.130       8.000
             Q1        Median   Q3 Maximum Range IQR
             10.500    11.800 13.825 17.900 9.900 3.325

             Mode      N for Mode Skewness Kurtosis MSSD
             11.8,11.5     3        0.52     -0.35   5.162




                             Boxplot of C1

      18



      16



      14
 C1




      12



      10



      8




                                 Box plot
The box plot represents the data set. This box plot shows that data is skewed
positively because the whisker is longer in upward side, which shows
positive skewness.
                                             Histogram (with Normal Curve) of C1
                                                                                              Mean 12.24
                              14
                                                                                              StDev 2.352
                                                                                              N        70
                              12

                              10
                  Frequency




                              8


                              6

                              4

                              2


                              0
                                        8       10        12         14        16        18
                                                                C1


                                   Histogram (with normal curve)
This normal curve graph shows that data is almost normally distributed.



                                            Histogram of C1

             14


             12

             10
 Frequency




             8


             6

             4

             2


             0
                  8                10          12          14             16        18
                                                     C1


HISTOGRAM
Formulas:

Cumulative percent=   ni n =100marks
                    Xi
Mean:  =      n = 12.244marks
The means shows the average of the data. This data set has the average

12.44

                                        s
Standard error of mean=                          = .281marks
                                            n


                                                       
                                                          2
                                                 i   
Standard deviation: s=                                        = 2.352 marks
                                             n 1

Variance: s
              2
                  =
                     i    2

                                   =5.530 marks
                       n 1
                                                     100  s
Coefficient of variation: C.V=                               =19.21 marks
                                                       
Sum=   i =857.100 marks
Sum of squares=   i2 =10876.130 marks
                                       th

First Quartile: Q1=   1 observation=10.500 marks
                      n
                        
                          4       

                          th

Median: Q2=   1 observation=11.800 marks
              n
                
            2 
Median is also used for average. T is to be noted that mode and median have
the same answers.


                                            th

Third Quartile: Q3= 
                            3n 
                              1 observation=13.825 marks
                            4   



Range=  m   o =9.900 marks
Interquartile Range: I.Q= Q3  Q1  =3.325 marks
Mode= The mode is the data value that occurs most often in the
dataset=11.5, 11.8 marks
The mode also tells us the average of the data


N for mode= N for Mode is the number of times the mode(s) appear(s) = 2
marks.

Skewness: b1=
                    n                  
                                           3

                               i   s  =0.52 marks
              n  1n  2             
This answer of skewness indicates that the data is positively skewed towards
the right side of the graph.


Kurtosis: b2=
                        nn  1                 4
                                                         3n  1
                                                                    2

                                         i   s   n  2n  3 =-0.35 marks
                 n  1n  2n  3             
Kurtosis shows that how different a distribution is from normal distribution.
This answer of kurtosis shows that it has flatter peak than normal
distribution because answer is negative.



                                                    11  1 2
Mean of Successive Squared Difference=
                                                                   2 =5.162 marks
                                                        n 1

								
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