Question

The daily income of a sample of $50$ employees are tabulated as follows :

Income (in Rs)	$1-200$	$201-400$	$401-600$	$601-800$
Number of employees	$14$	$15$	$14$	$7$

Find the mean of daily income of employees.

Answer 1

We can find the mean of daily income of employees using assumed mean method.

Step 1.Make frequency distribution table for given data.

Class Interval	$x_i$	$d_i=(x_i-A)$	$f_i$	$f_i{d}_i$
$1-200$	$100.5$	$-200$	$14$	$-2800$
$201-400$	$A=300.5$	$0$	$15$	$0$
$401-600$	$500.5$	$200$	$14$	$2800$
$601-800$	$700.5$	$400$	$7$	$2800$
			$\sum _{}^{}{f}_i=50$	$\sum _{}^{}{f}_i{d}_i=2800$

Where $A=300.5$ is assumed mean.

$f_i$ is frequency of $i^{th}$ class.

$d_i$ is deviation of $i^{th}$ class.

$x_i=\frac{upperlimt-lowerlimit}{2}$ is class marks

Step 2. Find the mean.

Since mean $=A+\frac{{\displaystyle \sum _{}^{}}{f}_i{d}_i}{{\displaystyle \sum _{}^{}}{f}_i}$ [Assumed mean formula]

Therefore we have ,

Mean of daily income of employees$=300.5+\frac{{\displaystyle 2800}}{{\displaystyle 50}}$

$$\begin{gathered} =300.5+56 \\ =356.5 \end{gathered}$$

Hence, the mean of daily income of employees is $Rs356.5$.