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જો માહિતી : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ નો મધ્યક $8$ હોય તો માહિતીનો વિચરણ મેળવો
$\frac{9}{8}$
$2$
$\frac{7}{8}$
$1$
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 $1$.
