If sum_{i = 1}^9 (x_i - 5) = 9 and sum_{i = 1 | vedclass

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(B) Let $y_i = x_i - 5$. Then $\sum_{i=1}^9 y_i = 9$ and $\sum_{i=1}^9 y_i^2 = 45$.The variance of a set of observations is invariant under change of

Vedclass · Accepted Answer

$2$

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(B) Let $y_i = x_i - 5$. Then $\sum_{i=1}^9 y_i = 9$ and $\sum_{i=1}^9 y_i^2 = 45$.The variance of a set of observations is invariant under change of origin. Therefore,the standard deviation of $x_i$ is the same as the standard deviation of $y_i$.Variance $(\sigma^2) = \frac{1}{n} \sum_{i=1}^n y_i^2 - \left( \frac{1}{n} \sum_{i=1}^n y_i \right)^2$$\sigma^2 = \frac{45}{9} - \left( \frac{9}{9} \right)^2$$\sigma^2 = 5 - 1 = 4$Standard deviation $(\sigma) = \sqrt{4} = 2$.

$x_i$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_i$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequencies	$5$	$8$	$15$	$16$	$6$

Marks of $A$	$30, 20, 40$
Marks of $B$	$70, 0, 5$

If $\sum_{i = 1}^9 (x_i - 5) = 9$ and $\sum_{i = 1}^9 (x_i - 5)^2 = 45$,then the standard deviation of the $9$ items $x_1, x_2, ..., x_9$ is:

Similar Questions

Find the mean and variance for the following data:

$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

$f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

Let $n$ observations $x_1, x_2, ....., x_n$ be such that $\sum {x_i}^2 = 400$ and $\sum x_i = 80$. Then,which of the following is a possible value for $n$?

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

Find the mean and variance for the following frequency distribution.

Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequencies $5$ $8$ $15$ $16$ $6$

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:

Marks of $A$ $30, 20, 40$

Marks of $B$ $70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

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