For 200 observations of a specific set of data, the mean was found to be 48 and the standard deviations is 3. Sum of squares of these 200 observations will be

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462600

462800

482600

462000

answer is B.

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Detailed Solution

$G i v e n t h a t t h e m e a n i s 48 H e n c e, \frac{\sum x_{i}}{200} = 48 T h e V a r i a n c e i s 9 H e n c e \frac{\sum x_{i}^{2}}{200} - {(\frac{\sum x_{i}}{200})}^{2} = 9$

$\Rightarrow \frac{\sum {x_{i}}^{2}}{200} = 9 + {(48)}^{2}$

$\Rightarrow \sum x_{i}^{2} = 462600$

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