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Question
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 |
Solution
The given data is shown as follows:
| Class | Frequency (f) | Class mark `(x_i)` | `f_i x_i` |
| 0 – 10 | 8 | 5 | 40 |
| 10 – 20 | p | 15 | 15p |
| 20 – 30 | 12 | 25 | 300 |
| 30 – 40 | 13 | 35 | 455 |
| 40 – 50 | 10 | 45 | 450 |
| Total | `sumf_i =43+ p` | `sum f_i x_i = 1245 + 15p` |
The mean of given data is given by x = `(sum_ i f_i x_i )/(sum_ i f_i)`
⇒ 27`= (1245 +15p)/(43+ p)`
⇒ 1161+27 p =1245 + 15 p
⇒ 27p - 15p = 1245 -1161
⇒ 12p=84
⇒ p=7
Thus, the value of p is 7.
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