Question

Find the mean salary of $60$ workers of a factory from the following table:

Salary in Rupees	Number of workers
$3000$	$16$
$4000$	$12$
$5000$	$10$
$6000$	$8$
$7000$	$6$
$8000$	$4$
$9000$	$3$
$10000$	$1$
Total	$60$

Answer 1

Calculate the mean of the workers' salary

Here, let us consider as salary of the workers as $x_i$ and the number of workers as the frequency $f_i$.

Salary in Rupees $\left(x_i\right)$	Number of workers $\left(f_i\right)$	${\mathit{f}}_{\mathbf{i}}{\mathit{x}}_{\mathbf{i}}$
$3000$	$16$	$48000$
$4000$	$12$	$48000$
$5000$	$10$	$50000$
$6000$	$8$	$48000$
$7000$	$6$	$42000$
$8000$	$4$	$32000$
$9000$	$3$	$27000$
$10000$	$1$	$10000$
Total	$\sum f_i=60$	$\sum f_i{x}_i=305000$

Thus, the mean of the worker's salary, $\overline{\mathbf{x}}\mathbf{=}\frac{\mathbf{\sum }{\mathbf{f}}_{\mathbf{i}}{\mathbf{x}}_{\mathbf{i}}}{\mathbf{\sum }{\mathbf{f}}_{\mathbf{i}}}$.

$$\begin{gathered} \Rightarrow \overline{x}=\frac{305000}{60} \\ \Rightarrow \overline{x}=5083.33 \end{gathered}$$

Therefore, the mean salary of workers is $5083.33$.