Question

Find the value of p, if the mean of the following distribution is 20.

x:	15	17	19	20+p	23
f:	2	3	4	5p	6

Answer 1

Given:

Mean

First of all prepare the frequency table in such a way that its first column consist of the values of the variate and the second column the corresponding frequencies.

Thereafter multiply the frequency of each row with corresponding values of variable to obtain third column containing.

Then, sum of all entries in the column second and denoted by and in the third column to obtain.

We know that mean,
$20=\frac{295+5p\left(20+p\right)}{15+5p}$

By using cross multiplication method,

$$\begin{gathered} 5p^2+100p+295=300+100p \\ \Rightarrow 5p^2=300-295=5 \\ \Rightarrow p^2=1 \\ \Rightarrow p=1 \end{gathered}$$

Hence, p