Question

Consider the following distribution of daily wages of $50$ workers of a factory.

Daily wages (in C)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer 1

Class interval	Mid-value $\left(X_i\right)$	Frequency $\left(f_i\right)$	$u_1=\frac{x_i-150}{20}$	$f_i{u}_i$
$100-120$	$110$	$12$	$-2$	$-24$
$120-140$	$130$	$14$	$-1$	$-14$
$140-160$	$150$	$8$	$0$	$0$
$160-180$	$170$	$6$	$1$	$6$
$180-200$	$190$	$10$	$2$	$20$
Total		$50$		$-12$

Lets take assumed mean, $A$ as $150$

Class interval $=20$

$\therefore u_i=\frac{x_i-A}{h}=\frac{x_i-150}{20}$

$\overline{x}=A+h\frac{\sum f_i{u}_i}{\sum f_i}=150+20\times \frac{-12}{50}=150-4.8=145.2$

Hence, mean is Rs $145.20$