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Find the missing value of $p$ for the following distribution whose mean is 12.58.
$x$ | 5 | 8 | 10 | 12 | $p$ | 20 | 25 |
$f$ | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Given:
The mean of the given data is 12.58.
To do:
We have to find the value of $p$.
Solution:
$x$ | $f$ | $f \times\ x$ |
5 | 2 | 10 |
8 | 5 | 40 |
10 | 8 | 80 |
12 | 22 | 264 |
$p$ | 7 | $7p$ |
20 | 4 | 80 |
25 | 2 | 50 |
Total | 50 | $524+7p$ |
We know that,
Mean$=\frac{\sum fx}{\sum f}$
Therefore,
Mean $12.58=\frac{524+7p}{50}$
$12.58(50)=524+7p$
$629=524+7p$
$7p=629-524$
$p=\frac{105}{7}$
$p=15$
The value of $p$ is $15$.
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