If each of the observations x_1, x_2, ldots, | vedclass

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(B) Let the original observations be $x_1, x_2, \ldots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$. If e

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does not change

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(B) Let the original observations be $x_1, x_2, \ldots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$. If each observation is increased or decreased by $k$,the new observations are $y_i = x_i \pm k$. The new mean becomes $\bar{y} = \frac{1}{n} \sum (x_i \pm k) = \bar{x} \pm k$. The new variance is $\sigma_y^2 = \frac{1}{n} \sum (y_i - \bar{y})^2 = \frac{1}{n} \sum ((x_i \pm k) - (\bar{x} \pm k))^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 = \sigma^2$. Thus,the variance remains unchanged.

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 each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:

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