Question

The following table gives the weekly wages of workers in a factory

Weekly Wages	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$	$75-80$	$80-85$	$85-90$
No. of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

Calculate

(i) the mean

Answer 1

Make the required frequency distribution table:

At first, we will prepare the table for values $x_i$and $f_i$ to find the value of$\sum _{}^{}{f}_i{x}_i$.

Class Interval	$x_i$	Frequency, $f_i$	$x_i{f}_i$
$50-55$	$52.5$	$5$	$262.5$
$55-60$	$57.5$	$20$	$1150$
$60-65$	$62.5$	$10$	$625$
$65-70$	$67.5$	$10$	$675$
$70-75$	$72.5$	$9$	$652.5$
$75-80$	$77.5$	$6$	$465$
$80-85$	$82.5$	$12$	$990$
$85-90$	$87.5$	$8$	$700$
Total		$\sum _{}^{}{f}_i=80$	$\sum _{}^{}{f}_i{x}_i=5520$

From the above table, we get the values of,

$\sum _{}^{}{f}_i=80$

$\sum _{}^{}{f}_i{x}_i=5520$

By substituting the obtained values in the Arithmetic mean formula,

we get, Arithmetic mean, $\overline{x}=\frac{{\sum }_{i=1}^n{x}_i{f}_i}{{\sum }_{i=1}^n{f}_i}$

$=\frac{5520}{80}$

$=69$

Hence, the mean for the given data is $\overline{x}=69.$