Question

Find the missing frequency p for the following frequency distribution whose mean is $28.25$.

Answer 1

We will prepare the following table:

From the table,

Mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

$\Rightarrow \frac{\sum f_i{x}_i}{\sum f_i}=28.25$

$\Rightarrow \frac{1445+25p}{50+p}=28.25$

$\Rightarrow 1445+25p=1412.5+28.25p$

$\Rightarrow 1445-1412.5=28.25p-25p$

$\Rightarrow 32.5=3.25p$

$\Rightarrow \frac{32.5}{3.25}=p$

$\Rightarrow 10=p$

Hence, the value of $p$ is $10$.