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Question
The mean of following frequency distribution is 54. Find the value of p.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 7 | p | 10 | 9 | 13 |
Solution
The given data is shown as follows:
| Class | Frequency`(f_i)` | Class mark `(x_i)` | `f_i x_i` |
| 0-20 | 7 | 10 | 70 |
| 20-40 | p | 30 | 30p |
| 40-60 | 10 | 50 | 500 |
| 60-80 | 9 | 70 | 630 |
| 80-100 | 13 | 90 | 1170 |
| Total | `sum f_i=39+p` | `sum f_i x_i = 2370 + 30p` |
The mean of the given data is given by,
x =`(sum_(i) f_i x_i)/(sum _(i)f_i)`
⇒ 54 =`(2370+30p)/(39+p)`
⇒ 54 (39 + p) = 2370 + 30p
⇒ 2106 + 54p = 2370 – 2106
⇒ 24p = 264
⇒ p = 11
Hence, the value of p is 11.
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