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  • For the frequency distribution: x 2 f 4 Find the standard distribution.

For the frequency distribution:

\begin{array}{|l|l|l|l|l|l|l|} \hline \mathrm{x} & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathrm{f} & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}

Find the standard distribution.

 

Answers (1)

A frequency distribution table is given and we have to find the standard deviation

 Let us make a table from the given data and fill out the other columns after calculation

\begin{array}{|l|l|l|l|} \hline \text { Size }\left(x_{i}\right) & \text { Frequency }\left(f_{i}\right) & f_{i} x_{i} & f_{i} x_{i}^{2} \\ \hline 2 & 4 & 8 & 16 \\ \hline 3 & 9 & 27 & 81 \\ \hline 4 & 16 & 64 & 256 \\ \hline 5 & 14 & 70 & 350 \\ \hline 6 & 11 & 66 & 396 \\ \hline 7 & 6 & 42 & 294 \\ \hline \text { Total } & \mathrm{N}=60 & 277 & 1393 \\ \hline \end{array}

\\\text{And we know that standard deviation is} \\\\ \sigma = \sqrt {\frac{ \Sigma f_{i}x_{i}^{2}}{n}- \left( \frac{ \Sigma f_{i}x_{i}}{n} \right) ^{2}}~ \\\\ \\ \text{Substituting the values from the above table } \sigma =\sqrt {\frac{1393}{60}- \left( \frac{277}{60} \right) ^{2}}=\sqrt {23.23-21.34}=1.37 \\\\

 

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