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Question

A polling agency interviewed 200 persons. The age distribution of those persons was recorded as under:
Age (Years) 80−89 70−79 60−69 50−59 40−49 30−39 20−29 10−19
Frequency 2 2 6 20 56 40 42 32
Calculate mean age of the persons by Direct Method.

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Solution

Age Mid Value (m)
m=l1+l22
Frequency
(f)
fm
10 − 19 10+192=14.5 32 464
20 − 29 20+292=24.5 42 1029
30 − 39 30+392=34.5 40 1380
40 − 49 40+492=44.5 56 2492
50 − 59 50+592=54.5 20 1090
60 − 69 60+692=64.5 6 387
70 − 79 70+792=74.5 2 149
80 − 89 80+892=84.5 2 169
Σf = 200 Σfm = 7160

Calculating the mean by Direct method:

X=ΣfmΣfor, X¯=7160200X¯=35.8

Hence,mean age of the persons is 35.8 years.

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