If the mean of the following data is 20.2, find the value of p.

We know that,

Mean $=\frac{\sum x_{i} f_{i}}{\sum f_{i}}$

For the following data:

Mean $=\frac{(10 \times 6)+(15 \times 8)+(20 \times p)+(25 \times 10)+(30 \times 6)}{6+8+p+10+6}$

$\Rightarrow 20.2=\frac{60+120+20 p+250+180}{30+p}$

$\Rightarrow 20.2(30+p)=610+20 p$

$\Rightarrow 606+20.2 p=610+20 p$

$\Rightarrow 20.2 p-20 p=610-606$

$\Rightarrow 0.2 p=4$

$\Rightarrow p=\frac{4}{0.2}$

$\Rightarrow p=\frac{40}{2}$

$\Rightarrow p=20$

Hence, the value of  p is 20.