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

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Question

(A) Given $n = 15$,$\sum x = 170$,and $\sum x^2 = 2830$.When the incorrect observation $20$ is replaced by $30$,the new sum $\sum x'$ is:$\sum x' = 17

Vedclass · Accepted Answer

$78$

Vedclass · Answer

(A) Given $n = 15$,$\sum x = 170$,and $\sum x^2 = 2830$.When the incorrect observation $20$ is replaced by $30$,the new sum $\sum x'$ is:$\sum x' = 170 - 20 + 30 = 180$.The new sum of squares $\sum x'^2$ is:$\sum x'^2 = 2830 - (20)^2 + (30)^2 = 2830 - 400 + 900 = 3330$.The variance is given by the formula $\sigma^2 = \frac{1}{n} \sum x'^2 - \left( \frac{\sum x'}{n} \right)^2$.Substituting the values:$\sigma^2 = \frac{3330}{15} - \left( \frac{180}{15} \right)^2$$\sigma^2 = 222 - (12)^2$$\sigma^2 = 222 - 144 = 78$.

In an experiment with $15$ observations on $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

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