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Question
If the mean of the following frequency distribution is 24, find the value of p.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 3 | 4 | p | 3 | 2 |
Solution
The given data is shown as follows:
| Class | Frequency`(f_i)` | Mid values`(x_i)` | `(f_i x_i)` |
| 0-10 | 3 | 5 | 15 |
| 10-20 | 4 | 15 | 60 |
| 20-30 | p | 25 | 25p |
| 30-40 | 3 | 35 | 105 |
| 40-50 | 2 | 45 | 90 |
| Total | `sum f_i = 12 +p` |
`sum f_i x_i = 270 +25p` |
The mean of the given data is given by,
x =`(sum_(i) f_i x_i)/(sum_(i) f_i )`
⇒24 = `(270+25p)/(12+p)`
⇒24 (12+p) = 270 + 25p
⇒ 288 + 24p = 270 + 25p
⇒ 25p - 24p = 288 -270
⇒p = 18
Hence, the value of p is 18.
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