The mean and variance of 8 observations are 1 | vedclass

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Question

$\bar{x}=10$

$\Rightarrow \bar{x}=\frac{63+a+b}{8}=10 \Rightarrow a+b=17$

since, variance is independent of origin. So, we subtract 10 from each

Vedclass · Accepted Answer

$7$

Vedclass · Answer

$\bar{x}=10$

$\Rightarrow \bar{x}=\frac{63+a+b}{8}=10 \Rightarrow a+b=17$

since, variance is independent of origin. So, we subtract 10 from each observation.

$So , \sigma^{2}=13.5=\frac{79+( a -10)^{2}+( b -10)^{2}}{8}-(10-10)^{2}$

$\Rightarrow a ^{2}+ b ^{2}-20( a + b )=-171$

$\Rightarrow a ^{2}+ b ^{2}=169 \quad \ldots(2)$

From

$(i) and (ii)$ $; a=12 \& b=5$

${x_i}$	$3$	$8$	$13$	$18$	$25$
${f_i}$	$7$	$10$	$15$	$10$	$6$

$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$

The mean and variance of $8$ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5,7,10,12,14,15,$ then the absolute difference of the remaining two observations is

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