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Question

Calculate the Coefficient of Variation for the following distribution of the wages of 200 workers in a factory:
Wages ( in ₹) : 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119
No. of workers : 11 23 40 60 35 16 9 6

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Solution

In order to calculate coefficient of variation, first we will convert the given inclusive series into exclusive series as follows:
Wages Mid Point
(m)
Frequency
(f)
fm Deviation from
x=m-XX=74.45
x2 fx2
39.5 − 49.5
49.5 − 59.5
59.5 − 69.5
69.5 − 79.5
79.5 − 89.5
89.5 − 99.5
99.5 − 109.5
109.5 − 119.5
44.5
54.5
64.5
74.5
84.5
94.5
104.5
114.5
11
23
40
60
35
16
9
6
489.5
1253.5
2580
4470
2957.5
1512
940.5
687
29.95
19.95
9.95
.05
10.05
20.05
30.05
40.05
897
398
99
.002
101
402
903
1604
9867
9154
3960
0.12
3535
6432
8127
9624
Σf = 200 Σfm = 14890 Σfx2 = 50699.12

X=ΣfmΣf=14890200=74.45SD σ=Σfx2Σf=50699.12200=253.4956=15.921Coefficient of variation=σX×100 =15.92174.45×100=1592.174.45 =21.38%

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