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Question
The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.
| Class interval | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
| Frequency | 7 | 6 | 9 | 13 | - | 5 | 4 |
Solution
Given mean = 18, let missing frequency be 'x'.
| Class interval | Mid value(x1) | Frequency(f1) | f1x1 |
| 11 - 13 | 12 | 7 | 84 |
| 13 - 15 | 14 | 6 | 84 |
| 15 - 17 | 16 | 9 | 144 |
| 17 - 19 | 18 | 13 | 234 |
| 19 - 21 | 20 | x | 20x |
| 21 - 23 | 22 | 5 | 110 |
| 23 - 25 | 24 | 4 | 96 |
| N = 44 + x | 752 + 20x |
Mean `=(sumf_1x_1)/N`
`18=(752+20x)/(44+x)`
(44 + x)18 = 752 + 20x
792 + 18x = 752 + 20x
20x - 18x = 792 - 752
2x = 40
x = 40/2 = 20
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