The mean and variance of 10 observations were | vedclass

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(C) Given $n = 10$,incorrect mean $\bar{x} = 15$,and incorrect variance $\sigma^2 = 15$.Incorrect sum of observations: $\sum x_i = n 	imes \bar{x} =

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given $n = 10$,incorrect mean $\bar{x} = 15$,and incorrect variance $\sigma^2 = 15$.Incorrect sum of observations: $\sum x_i = n 	imes \bar{x} = 10 	imes 15 = 150$.Correct sum of observations: $\sum x_{i, 	ext{correct}} = 150 - 25 + 15 = 140$.Correct mean: $\bar{x}_{	ext{correct}} = \frac{140}{10} = 14$.Using the variance formula $\sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2$,we have $15 = \frac{\sum x_i^2}{10} - 15^2$.$\frac{\sum x_i^2}{10} = 15 + 225 = 240 \implies \sum x_i^2 = 2400$.Correct sum of squares: $\sum x_{i, 	ext{correct}}^2 = 2400 - 25^2 + 15^2 = 2400 - 625 + 225 = 2000$.Correct variance: $\sigma_{	ext{correct}}^2 = \frac{\sum x_{i, 	ext{correct}}^2}{n} - (\bar{x}_{	ext{correct}})^2 = \frac{2000}{10} - 14^2 = 200 - 196 = 4$.Correct standard deviation: $\sigma_{	ext{correct}} = \sqrt{4} = 2$.

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

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Class	$10-20, 20-30, 30-40$
Frequency	$2, x, 2$

The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then,the correct standard deviation is $.....$

Similar Questions

Find the mean and variance for the following data:

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

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

Find the variance and standard deviation for the following data:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

The variance of $20$ observations is $5$. If each observation is multiplied by $3$ and then $8$ is added to each number,then the variance of the resulting observations is:

In a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then:

If the variance of the following frequency distribution is $50$,then $x$ is equal to:

Class $10-20, 20-30, 30-40$

Frequency $2, x, 2$

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