If the mean of the following distribution is 27, find the value of p.
| Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequency | 8 | p | 12 | 13 | 10 |
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Solution
| Class interval | Mid value(x1) | Frequency(f1) | f1x1 |
| 0 - 10 | 5 | 8 | 40 |
| 10 - 20 | 15 | p | 15p |
| 20 - 30 | 25 | 12 | 300 |
| 30 - 40 | 35 | 13 | 455 |
| 40 - 50 | 45 | 10 | 450 |
| N = 43 + p | `sumf_1x_1=1245 + 15p` |
Given
Mean = 27
`rArr(sumf_1x_1)/N=27`
`rArr(1245 + 15p)/(43+p)=27`
1245 + 15p = 27(43 + p)
1245 + 15p = 27p + 1161
27p - 15p = 1245 - 1161
12p = 84
p = 84/12 = 7
Concept: Mean of Grouped Data
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