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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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a

8.25

b

8.00

c

9.00

d

8.50

answer is D.

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Detailed Solution

$\begin{array}{rcl} n & = & 100, \sum x_{i} = 400, \sum {x_{i}}^{2} = 2475 \\ \sum x_{i} - (3 + 4 + 5) & = & 400 - 12 = 388 \\ x & = & New Mean = \frac{388}{97} = 4 \\ \sum x^{2} & = & \sum {x_{i}}^{2} = (3^{2} + 4^{2} + 5^{2}) = 2475 - 50 = 2425 \\ Variance & = & \frac{\sum x^{2}}{n} - {(x)}^{2} = \frac{2425}{97} - 16 \\ = & 25 - 16 \\ = & 9 \end{array}$

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