If the mean of the following distribution is 27, find the value of p.

Given: Mean = 27

Let the assumed mean A = 25 and h = 10.

We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$

Now, we have $\sum f_{i}=43+p, \sum f_{i} u_{i}=17-p, h=10$ and $A=25$

Putting the values in the above formula, we have

$27=25+10\left(\frac{1}{43+p} \times(17-p)\right)$

$\frac{2}{10}=\left(\frac{(17-p)}{43+p}\right)$

$43+p=85-5 p$

$6 p=42$

$p=7$