The variance of 20 observation is 5 . If each | vedclass

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Question

$\frac{1}{{20}}\sum\limits_{i = 1}^{20} {{{\left( {{x_i} - \bar x} \right)}^2} = 5} $

$\sum\limits_{i = 1}^{20} {{{\left( {{x_i} - \bar x} \right)}

Vedclass · Accepted Answer

$20$

Vedclass · Answer

$\frac{1}{{20}}\sum\limits_{i = 1}^{20} {{{\left( {{x_i} - \bar x} ight)}^2} = 5} $

$\sum\limits_{i = 1}^{20} {{{\left( {{x_i} - \bar x} ight)}^2} = 100} $

new observations are $2 \mathrm{x}_{1}, 2 \mathrm{x}_{2}, \ldots \ldots, 2 \mathrm{x}_{20}$

Their mean $=\overline{\mathrm{x}}_{1}=\frac{2\left(\mathrm{x}_{1}+\mathrm{x}_{2}+\ldots+\mathrm{x}_{20}ight)}{20}=2 \overline{\mathrm{x}}$

Now, variance$ = \frac{1}{{20}}\sum\limits_{i = 1}^{20} {{{\left( {2{x_i} - 2\bar x} ight)}^2}} $

$ = \frac{1}{{20}} 	imes 4\sum\limits_{i = 1}^{20} {{{\left( {{x_i} - \bar x} ight)}^2}} $

$ = \frac{1}{{20}} 	imes 4 	imes 100 = 20$

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

$X$	$c$	$2c$	$3c$	$4c$	$5c$	$6c$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

The variance of $20$ observation is $5$ . If each observation is multiplied by $2$ , then the new variance of the resulting observations, is

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