Question

Calculate coefficient of variation of the following series:

$\begin{array}{ccccccccccc}\text{S. No}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ \text{Frequency}& 53& 58& 25& 30& 54& 42& 32& 48& 46& 52\end{array}$

Answer 1

$\begin{array}{cccc}\text{S.No}& \text{Marks (X)}& \text{Deviation from mean}& \text{Square of deviations}\\ & & (x=X-\overline{X})where\overline{X}=44& (X-\overline{X}{)}^{2}or{x}^2\\ 1& 53& 9& 81\\ 2& 58& 14& 196\\ 3& 25& -19& 361\\ 4& 30& -14& 196\\ 5& 54& 10& 100\\ 6& 42& -2& 4\\ 7& 32& -12& 144\\ 8& 48& 4& 16\\ 9& 46& 2& 4\\ 10& 52& 8& 64\\ N=10& \sum X=440& & \sum x^2=1166\end{array}$

$\overline{X}=\frac{\sum X}{N}=\frac{440}{10}=4.4$

$\sigma x=\sqrt{\frac{\sum x^2}{N}}=\sqrt{\frac{1166}{10}}=\sqrt{116.6}=10.8$

$C.V=\frac{\sigma x}{\overline{X}}\times 100=\frac{10.8}{44}\times 100=24.54$