Page 162 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

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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