Question

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Answer 1

$N=10,\sum X=100,\sum X^2=1090CoefficientofVariation(C.V)=\frac{{\sigma }_X}{\overline{X}}\times 100\text{Mean}=\overline{X}=\frac{\sum X}{N}\text{Mean}=\frac{100}{10}=10{\sigma }_X^2=\frac{\sum X^2}{N}-(\overline{X}{)}^2{\sigma }_X^2=\frac{1090}{10}-{10}^2=109-100=9{\sigma }_X=\sqrt{9}=3.\therefore C.V=\frac{3}{10}\times 100=30$