Question

Find the mean of the distribution: Class $1-3,3-5,5-7,7-10$, Frequency $9,22,27,17$.

Answer 1

Step 1: Make the required frequency distribution formula

Class	Class marks $\left(x_i\right)$	Frequency $\left(f_i\right)$	$f_i{x}_i$
$1-3$	$2$	$9$	$18$
$3-5$	$4$	$22$	$88$
$5-7$	$6$	$27$	$162$
$7-10$	$8.5$	$17$	$144.5$
		$\underset{}{\sum f_i=75}$	$\underset{}{\sum f_i{x}_i=412.5}$

Step 2: Find the mean of given distribution

$\begin{array}{rcl}Mean\overline{x}& =& \frac{{\displaystyle \sum _{}}{f}_i{x}_i}{{\displaystyle \sum _{}}{f}_i}\\ & =& \frac{412.5}{75}\\ & =& 5.5\end{array}$

Hence, the mean of the given data is $5.5$.