Question

If the mean of the following data is 18.75, find the value of 'p'? x 10 15 p 25 30 frequency 5 10 7 8 2 ​

Answer 1

Given,

$\[mean = 18.75\]$

Data, $\[x = 10,15,p,25,30\]$

frequency, $\[f = 5,10,7,8,2\]$

Solution,

$\[mean = \frac{{\sum {fx} }}{{\sum f }}\]$

$\[ \Rightarrow 18.75 = \frac{{10 \times 5 + 15 \times 10 + p \times 7 + 25 \times 8 + 30 \times 2}}{{5 + 10 + 7 + 8 + 2}}\]$

Simplify it,

$\[\begin{array}{l} \Rightarrow 18.75 = \frac{{50 + 150 + 7p + 200 + 60}}{{32}}\\ \Rightarrow 18.75 = \frac{{7p + 460}}{{32}}\\ \Rightarrow 7p + 460 = 18.75 \times 32\\ \Rightarrow 7p = 140\\ \Rightarrow p = 20\end{array}\]$

Hence the value of p is 20.