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Find the value of $p$ for the following distribution whose mean is 16.6.
$x$: | 8 | 12 | 15 | $p$ | 20 | 25 | 30 |
$f$: | 12 | 16 | 20 | 24 | 16 | 8 | 4. |
Given:
The mean of the given data is 16.6.
To do:
We have to find the value of $p$.
Solution:
$x$ | $f$ | $f \times\ x$ |
8 | 12 | 96 |
12 | 16 | 192 |
15 | 20 | 300 |
$p$ | 24 | $24p$ |
20 | 16 | 320 |
25 | 8 | 200 |
30 | 4 | 120 |
Total | 100 | $1228+24p$ |
We know that,
Mean$=\frac{\sum fx}{\sum f}$
Therefore,
Mean $16.6=\frac{1228+24p}{100}$
$16.6(100)=1228+24p$
$1660=1228+24p$
$24p=1660-1228$
$p=\frac{432}{24}$
$p=18$
The value of $p$ is $18$.
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