Page 160 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 7: Measures of Dispersion

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

Class Intervals : 40-60 30-40 20-30 15-20 10-15 5-10 3-5 0-3
Frequency : 25 15 12 8 6 4 3 2
Solution:
Since mode is ill defined, skewness will be computed by the use of the median.

Calculation of X , and M
d
Class Freq. M.V. 2 Less than
d X 25 fd fd
Intervals (f ) (X) (c.f.)
0-3 2 1.5 23.5 47.0 1104.5 2
3-5 3 4.0 21.0 63.0 1323.0 5
5-10 4 7.5 17.5 70.0 1225.0 9
10-15 6 12.5 12.5 75.0 937.5 15
15-20 8 17.5 7.5 60.0 450.0 23
20-30 12 25.0 0.0 0.0 0.0 35
30-40 15 35.0 10.0 150.0 1500.0 50
40-60 25 50.0 25.0 625.0 15625.0 75
Total 75 460.0 22165.0

460
1. X 25 31.13
75

2
22165 460
2. 16.06
75 75
N 75
3. Since 37.5 , median class is 30 - 40.
2 2

Thus, = 30, = 35, = 15, = 10

37.5 35
M 30 10 31.67
d
15
3 X M 3 31.13 31.67
Also S d 0.10
k
16.06
Example: Calculate Bowley's coefficient of skewness from the following data:

ClassIntervals : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
Frequency : 7 10 20 13 17 10 14 9

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