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
$\left(\bar{x}\right)=A+\frac{\Sigma f_{i}y_{i}}{N}\times h=27.5+\frac{8}{100}\times5$
$=27.5+0.4=27.9$
Standard deviation
$\left(\sigma\right)=\frac{h}{N}\sqrt{N\,\Sigma f_{i}y_{i}^{2}-\left(\Sigma\,f_{i}y_{1}\right)^{2}}$
$\sigma=\frac{5}{100}\sqrt{100\times150-\left(8\right)^{2}}=\frac{1}{20}\sqrt{1500-64}
=\frac{1}{20}\times122.21=6.11$
$\therefore C.V.=\frac{\sigma}{\bar{x}}\times100$
$=\frac{6.11}{27.9}\times100=21.89$.