In an experiment with 15 observations of x,th | vedclass

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(B) Given $n = 15, \Sigma x = 170, \Sigma x^2 = 2830$.When an incorrect observation $20$ is replaced by the correct value $30$:Correct sum of observat

Vedclass · Accepted Answer

$78$

Vedclass · Answer

(B) Given $n = 15, \Sigma x = 170, \Sigma x^2 = 2830$.When an incorrect observation $20$ is replaced by the correct value $30$:Correct sum of observations $= 170 - 20 + 30 = 180$.Correct sum of squares of observations $= 2830 - 20^2 + 30^2 = 2830 - 400 + 900 = 3330$.Correct mean $\bar{x} = \frac{180}{15} = 12$.Correct variance $\sigma^2 = \frac{\Sigma x^2}{n} - (\bar{x})^2 = \frac{3330}{15} - (12)^2$.$\sigma^2 = 222 - 144 = 78$.

$x_i$	$92$	$93$	$97$	$98$	$102$	$104$	$109$
$f_i$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

$x_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

In an experiment with $15$ observations of $x$,the results $\Sigma x^2 = 2830$ and $\Sigma x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

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