Question

Find the $C.V.$ of the following data :

Size (in m)n	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$
No. of items	$2$	$8$	$20$	$35$	$20$	$15$

• A. $20.24$
• B. $21.89$
• C. $23.10$
• D. $19.20$

Answer 1

Answer: (B)

Here $h=5$, let $A$ (Assumed mean) $=27.5$


Mean
$\left(\bar{x}\right)=A+\frac{\Sigma f_i{y}_i}{N}\times h=27.5+\frac{8}{100}\times 5$
$=27.5+0.4=27.9$
Standard deviation
$\left(\sigma \right)=\frac{h}{N}\sqrt{N\Sigma f_i{y}_i^2-{\left(\Sigma f_i{y}_1\right)}^2}$
$\sigma =\frac{5}{100}\sqrt{100\times 150-{\left(8\right)}^2}=\frac{1}{20}\sqrt{1500-64}<br/>=\frac{1}{20}\times 122.21=6.11$
$\therefore C.V.=\frac{\sigma }{\bar{x}}\times 100$
$=\frac{6.11}{27.9}\times 100=21.89$.