Question

Find out the mean for the following data by direct method

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$9$	$12$	$15$	$10$	$14$

Answer 1

Make the required frequency distribution table.

First, we have to prepare a table to find the value of $\sum _{}{f}_i{x}_{i,}$

Class interval	Frequency $\left(f_i\right)$	Mid value$\left(x_i\right)$	$f_i$$x_i$
$0-10$	$9$	$5$	$45$
$10-20$	$12$	$15$	$180$
$20-30$	$15$	$25$	$375$
$30-40$	$10$	$35$	$350$
$40-50$	$14$	$45$	$630$
	$\sum _{}{f}_i=60$		$\sum _{}{f}_i{x}_{i,}=1580$

Calculate Mean.

From the table, we get the values of,

$\sum _{}{f}_i{x}_{i,}=1580$

$\sum _{}{f}_i=60$

Substitute the values in the arithmetic mean formula,

Then,

Arithmetic Mean$=\frac{\sum _{}{f}_i{x}_i}{\sum _{}{f}_i}$

$=\frac{1580}{60}=26.33$

Hence the arithmetic mean of the given distribution is $26.33$.