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

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(C) Let the observations be $x_1, x_2, \dots, x_{20}$ with mean $\bar{x}$.Given,variance $\sigma^2 = \frac{1}{20} \sum_{i=1}^{20} (x_i - \bar{x})^2 =

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$20$

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(C) Let the observations be $x_1, x_2, \dots, x_{20}$ with mean $\bar{x}$.Given,variance $\sigma^2 = \frac{1}{20} \sum_{i=1}^{20} (x_i - \bar{x})^2 = 5$.When each observation is multiplied by a constant $k=2$,the new observations are $y_i = 2x_i$.The new mean is $\bar{y} = 2\bar{x}$.The new variance is $\sigma_{new}^2 = \frac{1}{20} \sum_{i=1}^{20} (y_i - \bar{y})^2$.Substituting $y_i = 2x_i$ and $\bar{y} = 2\bar{x}$:$\sigma_{new}^2 = \frac{1}{20} \sum_{i=1}^{20} (2x_i - 2\bar{x})^2 = \frac{1}{20} \sum_{i=1}^{20} 4(x_i - \bar{x})^2$.$\sigma_{new}^2 = 4 	imes \left[ \frac{1}{20} \sum_{i=1}^{20} (x_i - \bar{x})^2 ight] = 4 	imes 5 = 20$.

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

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