Question

Calculate coefficient of variation from the following data :

$\begin{array}{cccccc}\text{No. of Goals Scored}& 0& 1& 2& 3& 4\\ \text{No. of Matches Played}& 27& 9& 8& 5& 4\end{array}$

Answer 1

$\overline{X}=A+\frac{\sum fd}{N}=2-\frac{50}{53}=2-0.94=1.06$

$\sigma =\sqrt{\frac{\sum f{d}^2}{N}-{\left(\frac{\sum fd}{N}\right)}^2}=\sqrt{\frac{138}{53}-{\left(\frac{-50}{53}\right)}^2}$

$=\sqrt{2.603-0.889}=\sqrt{1.714}=1.309$

C.V. $=\frac{\sigma }{\overline{X}}\times 100=\frac{1.309}{1.06}\times 100$

$=123.49\%$