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  4. 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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Q. 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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Solution:

$\displaystyle\sum_{i=1}^{100} x i= 400 \displaystyle\sum_{i=1}^{100} xi ^{2}=2475$
variance $\sigma^{2}=\frac{\sum x i^{2}}{N}-\left(\frac{\sum x_{1}}{N}\right)^{2} 3^{2}+4^{2}+5^{2}$
$9+16+25+50$
$=\frac{2475}{97}-\left(\frac{388}{97}\right)^{2}$
$\frac{2425}{97}-16$
$\frac{2425-1552}{97}=\frac{873}{97}$
$=(9)$