Question

Calculate the coefficient of variation for the following data :

$\begin{array}{cccccc}\text{Weight (kg)}& 0-20& 20-40& 40-60& 60-80& 80-00\\ \text{No. of Persons}& 81& 40& 66& 49& 14\end{array}$

Answer 1

$\overline{X}=A+\frac{\sum f{d}^{{}^{\prime }}}{N}\times i=50+\frac{(-125)}{250}\times 20=40$

$\sigma =\sqrt{\frac{\sum f{d}^{{}^{\prime 2}}}{N}-{\left(\frac{\sum f{d}^{{}^{\prime }}}{N}\right)}^2}\times i$

$=\sqrt{\frac{469}{250}-{\left(\frac{-125}{250}\right)}^2}\times 20$

$=\sqrt{1.876-0.25}\times 20=25.50$

$\therefore C.V=\frac{\sigma }{\overline{X}}\times 100=\frac{25.50}{40}\times 100=63.75\%$