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Unit 7: Measures of Dispersion




                                                                                                Notes
                 Example: Calculate the Kelly's coefficient of skewness from the following data :

                            Wages ( ) No.of Workers   Wages ( ) No.of Workers
                             800-900      10          1200-1300     160
                             900-1000     33          1300-1400      80
                            1000-1100     47          1400-1500      60
                            1100-1200    110
          Solution:
                                     Calculation of P , P  and P
                                                 10   50   90
                           Class Intervals No.of Workers (f ) Less than (c.f.)
                              800-900          10              10
                             900-1000          33              43
                            1000-1100          47              90
                            1100-1200         110             200
                            1200-1300         160             360
                            1300-1400          80             440
                            1400-1500          60             500
                               Total          500

                     10    10 500
          1.   Since    N           50,  10  lies in the interval 1000 - 1100.
                    100      100

               Thus,  L P  1000, C  43, f  47, h 100
                      10             10 P
                               50 43
                         1000          100 Rs 1014.89
               Hence,   10                    1014.89
                                 47
                     50
          2.   Since    N = 250 ,    lies in the interval 1200 - 1300.
                     100          50
               Thus, L  =1200, C = 200, f  =160, h =100
                     P 50              P 50
                               250 200
                         1200            100 Rs  1231.25
               Hence,   50                      12.31.25
                                  160
                    90
          (iii)  Since   N = 450,   90  lies in the class 1400 - 1500.
                    100
               Thus,  L P  =1400, C = 440, f P  =60, h =100.
                      90                90
                               450 440
                         1400            100 Rs  1416.67
                                                 14.16.67
               Hence,   90
                                  60
                     1416.67 1014.89 2 1231.25     30.94
                  S P                                      0.08
                           1416.67 1014.89       401.78

                 Example: Compute the moment measure of skewness from the following distribution.
                Marks obtained : 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 -70
                No. of Students :  8     14     22     26      15     10      5






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