The variance of the data $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$ is

15

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20

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30

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33

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Solution

The correct option is D $33$
Mistake : $14$ is not given
Mean $¯ x = \frac{6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{10} = \frac{150}{10} = 15$
Variance $= \frac{1}{n} n \sum i = 1 (x_{i} - ¯ x)^{2}$
$⟹ \frac{1}{10} ((6 - 15)^{2} + (8 - 15)^{2} + (10 - 15)^{2} + (12 - 15)^{2} + (14 - 15)^{2} + (16 - 15)^{2} + (18 - 15)^{2} + (20 - 15)^{2}$
$+ (22 - 15)^{2} + (24 - 15)^{2}$

$⟹ \frac{81 + 49 + 25 + 9 + 1 + 1 + 9 + 25 + 49 + 81}{10}$

$⟹ \frac{330}{10} = 33$

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