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

Vedclass · Accepted Answer

Origin only

Vedclass · Answer

(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.

Class Interval	$0$-$5$	$5$-$10$	$10$-$15$	$15$-$20$	$20$-$25$
Frequency	$4$	$1$	$10$	$3$	$2$

$x_i$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_i$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

$C$.$I$.	$75$-$175$	$175$-$275$	$275$-$375$	$375$-$475$	$475$-$575$	$575$-$675$	$675$-$775$
$f_i$	$3$	$2$	$1$	$0$	$1$	$2$	$3$

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

Similar Questions

For the following frequency distribution,the variance is approximately equal to
Class Interval $0$-$5$ $5$-$10$ $10$-$15$ $15$-$20$ $20$-$25$
Frequency $4$ $1$ $10$ $3$ $2$

Find the variance of the following discrete frequency distribution:
Class Interval $0-2$ $2-4$ $4-6$ $6-8$ $8-10$
Frequency $(f_i)$ $2$ $3$ $5$ $3$ $2$

The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
$f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

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Consider the following frequency distribution:
$C$.$I$. $75$-$175$ $175$-$275$ $275$-$375$ $375$-$475$ $475$-$575$ $575$-$675$ $675$-$775$
$f_i$ $3$ $2$ $1$ $0$ $1$ $2$ $3$
If the variance of this distribution is $60000$,then the coefficient of variation of the distribution is:

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt{5}$ where $k > 0$,then $k$ is equal to

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