The sum of 100 observations and the sum of th | vedclass

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(D) Given: $N = 100$,$\sum x_i = 400$,$\sum x_i^2 = 2475$. Removing incorrect observations $3, 4, 5$: New sum $\sum x_i' = 400 - (3 + 4 + 5) = 400 - 1

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$9$

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(D) Given: $N = 100$,$\sum x_i = 400$,$\sum x_i^2 = 2475$. Removing incorrect observations $3, 4, 5$: New sum $\sum x_i' = 400 - (3 + 4 + 5) = 400 - 12 = 388$. New sum of squares $\sum (x_i')^2 = 2475 - (3^2 + 4^2 + 5^2) = 2475 - (9 + 16 + 25) = 2475 - 50 = 2425$. New number of observations $N' = 100 - 3 = 97$. Variance $\sigma^2 = \frac{\sum (x_i')^2}{N'} - \left( \frac{\sum x_i'}{N'} ight)^2$. $\sigma^2 = \frac{2425}{97} - \left( \frac{388}{97} ight)^2$. Since $388 = 4 	imes 97$,$\frac{388}{97} = 4$. $\sigma^2 = 25 - (4)^2 = 25 - 16 = 9$.

The sum of $100$ observations and the sum of their squares are $400$ and $2475$,respectively. Later on,three observations,$3, 4$ and $5$,were found to be incorrect. If the incorrect observations are omitted,then the variance of the remaining observations is

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