If the mean of the data : 7, 8, 9, 7, 8, 7,&n | vedclass

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Question

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

Vedclass · Accepted Answer

$1$

Vedclass · Answer

$\left( d ight)\,\,\bar x = \frac{{7 + 8 + 9 + 7 + 8 + 7 + \lambda  + 8}}{8} = 8$

           $ \Rightarrow \frac{{54 + \lambda }}{8} = 8 \Rightarrow \lambda  = 10$

Now variance $ = {\sigma ^2}$

$ = \frac{\begin{array}{l}
{\left( {7 - 8} ight)^2} + {\left( {8 - 8} ight)^2} + {\left( {9 - 8} ight)^2} + {\left( {7 - 8} ight)^2} + {\left( {8 - 8} ight)^2}\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + {\left( {7 - 8} ight)^2} + {\left( {10 - 8} ight)^2} + {\left( {8 - 8} ight)^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 $1$.

Height in cms	$70-75$	$75-80$	$80-85$	$85-90$	$90-95$	$95-100$	$100-105$	$105-110$	$110-115$
No. of children	$3$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

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

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