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Find the missing frequency $p$ for the following distribution whose mean is 7.68.
$x$: | 3 | 5 | 7 | 9 | 11 | 13 |
$f$: | 6 | 8 | 15 | $p$ | 8 | 4. |
Given:
The mean of the given data is 7.68.
To do:
We have to find the value of $p$.
Solution:
$x$ | $f$ | $f \times\ x$ |
3 | 6 | 18 |
5 | 8 | 40 |
7 | 15 | 105 |
9 | $p$ | $9p$ |
11 | 8 | 88 |
13 | 4 | 52 |
Total | $41+p$ | $303+9p$ |
We know that,
Mean$=\frac{\sum fx}{\sum f}$
Therefore,
Mean $7.68=\frac{303+9p}{41+p}$
$7.68(41+p)=303+9p$
$314.88+7.68p=303+9p$
$9p-7.68p=314.88-303$
$p=\frac{11.88}{1.32}$
$p=\frac{1188}{132}$
$p=9$
The value of $p$ is $9$.
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