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

Daily Pocket Allowence(in Rs) 11-13 13-15 15-17 17-19 19-21 21-23 23-35

Number of children 7 6 9 13 f 5 4

Question

Accepted Answer

Answer :

Given, \( \overline{x} \ = \ 18 \)

Class interval	Number of children (frequency (\(f_i\)) )	Mid-point \( (x_i) \)	\(f_i u_i \)
11-13	7	12	84
13-15	6	14	84
15-17	9	16	144
17-19	13	18	234
19-21	f	20	20f
21-23	5	22	110
23-25	4	24	96
Total	\( \sum f_i \ = \ 44 \ + \ f \)		\( \sum f_i x_i \ = \ 752 \ + \ 20f \)

Thus, \( \ \overline{x} \ = \ \frac{ \sum \ f_i x_i}{ \sum f_i} \)

\( \Rightarrow \ 18 \ = \ \frac{752 \ + \ 20f}{44 \ + \ f} \)

\(\Rightarrow \ 18(44 \ + \ f) \ = \ (752 \ + \ 20f) \)

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

\( \Rightarrow \ 792 \ - \ 752 \ = \ 20f \ - \ 18f \ \)
\( \Rightarrow \ 40 \ = \ 2f \)

\(\Rightarrow \ f \ = \ 20 \)

So, the missing frequency, f = 20.

Daily Pocket Allowence(in Rs)	11-13	13-15	15-17	17-19	19-21	21-23	23-35
Number of children	7	6	9	13	f	5	4

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