Mathematics
If the mean of the following observations is 16.6, find the numerical value of p.
| Variate (xi) | Frequency (fi) |
|---|---|
| 8 | 12 |
| 12 | 16 |
| 15 | 20 |
| 18 | p |
| 20 | 16 |
| 25 | 8 |
| 30 | 4 |
Measures of Central Tendency
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Answer
| Variate (xi) | Frequency (fi) | fi xi |
|---|---|---|
| 8 | 12 | 96 |
| 12 | 16 | 192 |
| 15 | 20 | 300 |
| 18 | p | 18p |
| 20 | 16 | 320 |
| 25 | 8 | 200 |
| 30 | 4 | 120 |
| Total | ∑fi = 76 + p | ∑ fixi = 1228 + 18p |
We know that,
n = ∑f = 76 + p.
By formula,
⇒ 16.6(76 + p) = 1228 + 18p
⇒ 1261.6 + 16.6p = 1228 + 18p
⇒ 1261.6 - 1228 = 18p - 16.6p
⇒ 33.6 = 1.4p
⇒ p =
⇒ p = 24.
Hence, numerical value of p is 24.
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