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 Interval	11 – 13	13 – 15	15 – 17	17 – 19	19 – 21	21 – 23	23 – 25
Frequency	7	6	9	13	f	5	4

Solution :

We have,

Class Interval	Mid-value (\(x_i\))	Frequency (\(f_i\))	\(f_ix_i\)
11 – 13	12	7	84
13 – 15	14	6	84
15 – 17	16	9	144
17 – 19	18	13	234
19 – 21	20	f	20 f
21 – 23	22	5	110
23 – 25	24	4	90
		\(\sum f_i\) = 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.