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If the mean of the following distribution is 27, find the value of $p$.
Class: | 0-8 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequency: | 8 | $p$ | 12 | 13 | 10 |
Given:
The mean of the given distribution is 27.
To do:
We have to find the value of $p$.
Solution:
Mean $=27$
We know that,
Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$
Therefore,
Mean $27=\frac{1245+15p}{43+p}$
$27(43+p)=1245+15p$
$1161+27p=1245+15p$
$1245-1161=27p-15p$
$p=\frac{84}{12}$
$p=7$
The value of $p$ is $7$.
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