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

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

Vedclass · Accepted Answer

$78$

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

In an experiment with $15$ observations of $x$,the results $\sum x^2 = 2830$ and $\sum x = 170$ 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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