The variance is independent of the change of | vedclass

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(A) Let the observations be $x_1, x_2, \dots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2$. If we change the origin

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Origin only

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(A) Let the observations be $x_1, x_2, \dots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2$. If we change the origin by a constant $a$,the new observations are $y_i = x_i + a$. The mean becomes $\bar{y} = \bar{x} + a$. The new variance is $\frac{1}{n} \sum (y_i - \bar{y})^2 = \frac{1}{n} \sum (x_i + a - (\bar{x} + a))^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 = \sigma^2$. Thus,the variance is independent of the change of origin. If we change the scale by a constant $b$,the new observations are $y_i = b x_i$. The new variance becomes $b^2 \sigma^2$. Therefore,the variance is independent of the change of origin only.

${x_i}$	$3$	$8$	$13$	$18$	$23$
${f_i}$	$7$	$10$	$15$	$10$	$6$

The variance is independent of the change of which of the following?

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