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  • The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is root52by7

The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is

A.\sqrt{\frac{52}{7}}

B.\frac{52}{7}

C.\sqrt{6}

D.6

Answers (1)

Given data can be written in table form as,

\begin{array}{|l|l|} \hline \text { Data }\left(x_{i}\right) & x_{i}^{2} \\ \hline 6 & 36 \\ \hline 5 & 25 \\ \hline 9 & 81 \\ \hline 13 & 169 \\ \hline 12 & 144 \\ \hline 8 & 64 \\ \hline 10 & 100 \\ \hline \text { Total }=63 & 619 \\ \hline \end{array}

\\ \text{But~we know that standard deviation can be written as } \\ \\ \sigma = \sqrt {\frac{ \Sigma x_{i}^{2}}{n}- \left( \frac{ \Sigma x_{i}}{n} \right) ^{2}}= \sqrt {\frac{619}{7}- \left( \frac{63}{7} \right) ^{2}}~~~ \\ \\ \sigma = \sqrt {\frac{619}{7}- \left( 9 \right) ^{2}}=\sqrt {\frac{619}{7}-81}~ =\sqrt {\frac{52}{7}} \\

 

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infoexpert21

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