The coefficient of variation of \(9,3,11,5,7\), is

The coefficient of variation of \(9,3,11,5,7\), is
  1. \(\frac{100 \sqrt{2}}{7}\)
  2. \(\frac{200 \sqrt{2}}{3}\)
  3. \(\frac{200 \sqrt{2}}{7}\)
  4. \(\frac{100 \sqrt{2}}{3}\)

Solution

Given numbers are 9, 3, 11, 5, 7. Now, mean \((\bar{x})=\frac{9+3+11+5+7}{5}=\frac{35}{5}=7\) Variance \(\sigma^2=\frac{1}{5}\left(9^2+3^2+11^2+5^2+7^2\right)-(7)^2\) \(\begin{aligned} & =\frac{1}{5}(81+9+121+25+49)-49 \\ & =\frac{285}{5}-49=57-49=8 \end{aligned}\) \(\therefore\) Coefficient of variation \(\frac{\sigma^2}{x} \times 100=\frac{\sqrt{8}}{7} \times 100=\frac{200 \sqrt{2}}{7}\)

Asked in: AP EAMCET 2019 (22 Apr Shift 1)

Practice more Statistics questions on Aicharya