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Question

The variance of first $$ 50$$ even natural numbers is


A
8334
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B
833
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C
437
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D
4374
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Solution

The correct option is A $$ 833$$
$$ \sigma ^{2}=\left (\displaystyle \frac{\Sigma x_{i}^{2}}{n} \right )-\bar{x}^{2}$$
$$ \displaystyle \bar{x}=\frac{\sum_{r=1}^{50}2r}{50}=51$$
$$ \sigma ^{2}= \displaystyle \frac{\sum_{r=1}^{50}4r^{2}}{50}-(51)^{2}=833$$

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