Question

Consider the above distribution of daily wages of $50$ worker of a factory.
Find the mean daily wages.

Answer 1

To find the class mark $x_i$ for each interval, using the following relation:

Class mark $x_i=\frac{\text{Upper class limit}+\text{Lower class limit}}{2}$

Class size $h=20$

Taking $150$ as assumed mean $a.$

Values of $d_i,u_i$ and $f_i{u}_i$ has been calculated in the table.

And,

$\sum f_i=50$

$\sum f_i{u}_i=-12$

So, mean will be equal to,

$\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)\times h$

$=150+\left(\frac{-12}{50}\right)\times 20$

$=150-\frac{24}{5}$

$=150-4.8$

$=145.2$

$\therefore$ The mean daily wage of the workers of the factory is equal to $\text{Rs.}145.20$.