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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 |
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.