If mean of data : 7, 8, 9, 7, 8, 7, mathop λ limits^. , 8 is 8 , then variance of this da

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13.Statistics

hard

If the mean of the data : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ is $8$, then the variance of this data is

$\frac{9}{8}$

$2$

$\frac{7}{8}$

$1$

(JEE MAIN-2018)

Solution

$\left( d \right)\,\,\bar x = \frac{{7 + 8 + 9 + 7 + 8 + 7 + \lambda + 8}}{8} = 8$

$ \Rightarrow \frac{{54 + \lambda }}{8} = 8 \Rightarrow \lambda = 10$

Now variance $ = {\sigma ^2}$

$ = \frac{\begin{array}{l}
{\left( {7 – 8} \right)^2} + {\left( {8 – 8} \right)^2} + {\left( {9 – 8} \right)^2} + {\left( {7 – 8} \right)^2} + {\left( {8 – 8} \right)^2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + {\left( {7 – 8} \right)^2} + {\left( {10 – 8} \right)^2} + {\left( {8 – 8} \right)^2}
\end{array}}{8}$

$ \Rightarrow {\sigma ^2} = \frac{{1 + 0 + 1 + 1 + 0 + 1 + 4 + 0}}{8} = \frac{8}{8} = 1$

Hence, the variance is $1$.

Standard 11

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