The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is 18 rupees. Find the missing frequency f.

Question :

Class Interval11 – 1313 – 1515 – 1717 – 1919 – 2121 – 2323 – 25
Frequency76913f54

Solution :

We have,

Class IntervalMid-value (\(x_i\))Frequency (\(f_i\))\(f_ix_i\)
11 – 1312784
13 – 1514684
15 – 17169144
17 – 191813234
19 – 2120f20 f
21 – 23225110
23 – 2524490
\(\sum f_i\) = 44 + f\(\sum f_ix_i\) = 752 + 20f

So, Mean (\(\bar{x}\)) = \(\sum f_ix_i\over f_i\) = \(752 + 20f\over 44 + f\)

\(\implies\) 18 = \(752 + 20f\over 44 + f\)

\(\implies\) 752 + 20f = 792 + 18f

\(\implies\) 2f = 40

\(\implies\) f = 20

Hence, the missing frequency is 20.

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