Question

The weights (in kg) of $50$wrestlers are recorded in the following table : Find the mean weight of the wrestlers.

Weight (in kg)	$100-110$	$110-120$	$120-130$	$130-140$	$140-150$
Number of wrestlers	$4$	$14$	$21$	$8$	$3$

Answer 1

Finding mean weight of the wrestlers:

We can find the mean weight of the wrestlers by using some methods . We solve this question by assumed mean method .

Weight (in kg)	Number of Wrestlers (fi)	Class Marks (xi)	Deviation (di = xi – a)	fidi
$100-110$	$4$	$105$	$-20$	$-80$
$110-120$	$14$	$115$	$-10$	$-140$
$120-130$	$21$	$125$	$0$	$0$
$130-140$	$8$	$135$	$10$	$80$
$140-150$	$3$	$145$	$20$	$60$
	$\text{N=}\underset{}{\sum \text{f=50}}$			$\sum _{}{\text{f}}_i{\text{d}}_i\text{= -80}$

Assumed mean ($\text{a}$)$=125$

Class width ($\text{h}$)$=10$

Total observations ($\text{N}$)$=50$

By step-deviation method ,

$\overline{x}=\text{a+}\frac{{\displaystyle \sum _{}}{\text{f}}_i{\text{d}}_i}{{\displaystyle \underset{}{\sum {\text{f}}_i}}}$

$=125+\frac{(-80)}{50}=125-\frac{80}{50}=\frac{125\times 50-80}{50}=\frac{6250-80}{50}=\frac{6170}{50}=123.4\text{kg}$

Hence, mean weight of wrestlers is $123.4\text{kg}$.