The standard deviation of the following distribution $\begin{aligned} \begin{array}{|c|c|c|c|} \hline ext{C.I.} & 0-6 & 6-12 & 12-18 \ \hline f_{i} & 2 & 4 & 6 \ \hline \end{array} \end{aligned}$ is

Question

The standard deviation of the following distribution $\begin{aligned} \begin{array}{|c|c|c|c|} \hline 	ext{C.I.} & 0-6 & 6-12 & 12-18 \ \hline f_{i} & 2 & 4 & 6 \ \hline \end{array} \end{aligned}$ is

Aicharya · Accepted Answer

$\begin{array}{|c|c|c|c|c|c|} \hline C.I. & \mathbf{f}_{i} & \mathbf{x}_{i} & \mathbf{x}_{i}^{2} & \mathbf{f}_{i} \mathbf{x}_{i} & \mathbf{f}_{i} \mathbf{x}_{i}^{2} \ \hline 0-6 & 2 & 3 & 9 & 6 & 18 \ \hline 6-12 & 4 & 9 & 81 & 36 & 324 \ \hline 12-18 & 6 & 15 & 225 & 90 & 1350 \ \hline 	ext{Total} & 12 & & & 132 & 1692 \ \hline \end{array}$ Here $\sum \mathrm{f}_{\mathrm{i}}=12, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}=132, \sum \mathrm{f}_{\mathrm{i}} x_{\mathrm{i}}^2=1692$ $\begin{aligned} 	herefore \quad \mathrm{V}(\mathrm{X}) & =\frac{1692}{12}-\left(\frac{132}{12}ight)^2 \ & =141-121 \ & =20 \end{aligned}$ $	herefore \quad$ Standard deviation $=\sqrt{20}=2 \sqrt{5}$

The standard deviation of the following distribution $\begin{aligned} \begin{array}{|c|c|c|c|} \hline…

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