Question

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

$x_i$	10	15	20	25	30
$f_i$	6	8	p	10	6

Answer 1

We have,

$x_i$	$f_i$	$f_i$$x_i$
10	6	60
15	8	120
20	p	20p
25	10	250
30	6	180
	Total N = (30 + p)	Total sum = (610 + 20p)

Since, mean = 20.2

$$\begin{gathered} \Rightarrow \frac{\left(610+20p\right)}{\left(30+p\right)}=20.2 \\ \Rightarrow 610+20p=20.2\left(30+p\right) \\ \Rightarrow 610+20p=606+20.2p \\ \Rightarrow 20.2p-20p=610-606 \\ \Rightarrow 0.2p=4 \\ \Rightarrow p=\frac{4}{0.2} \\ \therefore p=20 \end{gathered}$$