The coefficient of variation for the frequency distribution is $\begin{array}{|c|c|c|c|}\hlinex_i & 4 & 3 &…

The coefficient of variation for the frequency distribution is $\begin{array}{|c|c|c|c|}\hlinex_i & 4 & 3 & 1 \\\hlinef_i & 1 & 3 & 5 \\\hline\end{array}$
  1. $\frac{50}{\sqrt{3}}$
  2. $\frac{125}{2 \sqrt{3}}$
  3. $\frac{100}{3 \sqrt{2}}$
  4. $\frac{100}{\sqrt{3}}$

Solution

$\begin{array}{|c|c|c|c|c|}\hline \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{f}_{\boldsymbol{i}} & \boldsymbol{f}_{\boldsymbol{i}} \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{D}=\boldsymbol{x}_{\boldsymbol{i}}-\boldsymbol{\mu} & \boldsymbol{f}_{\boldsymbol{i}} \boldsymbol{D}^{\mathbf{2}} \\\hline 4 & 1 & 4 & 2 & 4 \\3 & 3 & 9 & 1 & 3 \\1 & 5 & 5 & -1 & 5 \\\hline & 9 & 18 & & 12 \\\hline\end{array}$
Mean $(\mu)=\frac{\sum f_i x_i}{\sum f_i}=\frac{18}{9}=2$ Standard deviation $(\sigma)=\sqrt{\frac{\sum f_i D^2}{\sum f_i}}=\sqrt{\frac{12}{9}}=\frac{2}{\sqrt{3}}$ Coefficient of variation $=\frac{\sigma}{\mu} \times 100=\frac{100}{\sqrt{3}}$.

Asked in: AP EAMCET 2024 (21 May Shift 2)

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