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 |
CLASS | MID - POINT(xi) | FREQUENCY(fi) | fixi |
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 |
TOTAL | 43 + p | 1245 + 15p |
We have got
Σfi = 43 + p and Σfixi = 1245 + 15p
∵ mean is given by
⇒ 
(∵ given: mean of pocket allowance is 27)
⇒ 1161 + 27p = 1245 + 15p
⇒ 27p – 15p = 1245 – 1161
⇒ 12p = 84
⇒ p = 84/12
⇒ p = 7
Thus, p = 7
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