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Question

In the following frequency distribution, ifthe arithmetic mean is 45.6, find out missing frequency.
Wages (₹) 10−20 20−30 30−40 40−50 50−60 60−70 70−80
Number of Workers 5 6 7 X 4 3 9

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Solution

Wages
(X)
Mid Value
(m)
No. of worker
(f)
fm
10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − 80
15
25
35
45
55
65
75
5
6
7
X
4
3
9
75
150
245
45
220
195
675
∑f = 34 + X ∑fm = 1560 + 45X

Substituting the values in the formula for mean.
X=ΣfmΣf45.6=1560 + 45X34 + Xor, 45.6 (34 + X) = 1560 + 45 Xor, 1550.4 + 45.6 X = 1560 + 45 Xor, 45.6 X − 45 X = 1560 1550.4or, 0.6X = 9.6or, X = 16

X=9.6.6
X = 16
Hence, the missing frequency is 16.

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