Session-5-measures-of-central-tendency by cuiliqing

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									Measures of Central Tendency
         (Contd…)
          Prepared by: Bhakti Joshi
          Date: November 28, 2011
   Frequency distribution of Weights in Pounds of a
                 sample of packages
                Frequency of
Weights Class                    Mid-point (x)          fx
                packages (f)
 10.0 – 10.9         1         (10+10.9)/2= 10.5   1*10.5= 10.5
 11.0 – 11.9         4               11.5           4*11.5= 46
 12.0 – 12.9         6               12.5           6*12.5=75
 13.0 – 13.9         8               13.5           8*13.5= 108
 14.0 – 14.9        12               14.5          12*14.5= 174
 15.0 – 15.9        11               15.5          11*15.5=170.5
 16.0 – 16.9         8               16.5           8*16.5=132
 17.0 – 17.9         7               17.5          7*17.5=122.5
 18.0 – 18.9         6               18.5           6*18.5=111
 19.0 – 19.9         2               19.5           2*19.5=39
                    65                                 988.5
                                                         15.2
       Monthly Average Cash Balances of 600
                    customers
                  Frequency of
Class (Rupees)                    Mid-point (x)        fx
                  Customers (f)
   0 – 49.9            78         (0+49.9)/2= 25   78*25= 1950
 50.00 - 99.99        123              75             9225
100.00 - 149.99       187              125           23375
150.00 - 199.99        82              175           14350
200.00 – 249.99        51              225           11475
250.00 – 299.99        47              275           12925
300.00 - 349.99        13              325            4225
350.00 – 399.99        9               375            3375
400.00 – 449.99        6               425            2550
450.00 – 499.99        4               475            1900
                      600                            85,350
                                                      142.25
                    Median
…Central Item of a data set
   Roll No.   Age

      1       18
      2       18
      3       18
                      (N+1) /2 = M
      4       18      N = Number of observations
      5       19      M= Median
      6       16
      7       18
      8       17
      9       18
      10      18
                             Median
            Frequency
   Age      of Mobile   Cumulative
Intervals    Phones     Frequency
            Owned (f)
 10 - 15       20          20
 15 - 20       40          60
 20 - 25       60          120
 25 - 30       70          190
 30 - 35       60          250
 35 - 40       30          280
 40 - 45       20          300


       Interpretation?
     Estimated median weight of the fish
                  caught
             Frequency
 Weights                  Cumulative   Item or number that represents
               of fish
 Intervals                Frequency    median
             caught (f)
10-19.5           8           8             383+1 / 2= 192nd item
20-29.5          15          23
30-39.5          23          46        Class that contains the median
40-49.5          37          83        item
50-59.5          46          129            70 – 79.5
60-69.5          52          181       Width of the weights interval
70-79.5          84          265             9.5
80-89.5          97          362        Estimated median value?
90-99.5          16          378             (192 – (181+1)   * 9.5 + 70 =
100-109.5         5          383                  84

                                                              71.13
                                Mode
…Value that is repeated most often in the data set. Mode is not used
for ungrouped data

            Frequency
   Age      of Mobile   Cumulative
Intervals    Phones     Frequency
            Owned (f)
 10 - 15       20          20
 15 - 20       40          60
 20 - 25       60          120
 25 - 30       70          190
 30 - 35       60          250
 35 - 40       30          280
 40 - 45       20          300

      Interpretation?
 Relationship between Mean-Median-
                Mode
• Mean < Median < Mode = Positively Skewed

• Mean> Median> Mode = Negatively Skewed

• Mean = Median = Mode = Normal
        Normal




Negatively (left)
Skewed




      Positively (right)
      Skewed
                     Projects
Stock Prices of Companies representing any one of the
following industries listed on the BSE or NSE
• Textiles
• Banking
• Automobiles
• IT/Telecommunication
• Pharmaceutical
• Foods & Beverages
• Infrastructure
• Steel
• Oil & Gas
• Chemicals
             Project Requirements
• Select 2 or more stocks of representative industry
• Stock prices of minimum 100 data points each
• Background of the representative companies
   –   Names
   –   Industry
   –   Occupation (Trading, manufacturing, distribution, etc)
   –   Products/services
   –   Customers
• Select statistical tools to compare and analyze the
  trends and performance of the stocks in the stock
  market
      Email: bhaktij@gmail.com
Website: www.headscratchingnotes.net
Frequency and Distribution Curve
Geometric Mean

								
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