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 $33$
$¯ ¯ ¯ x = \frac{6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{10} = \frac{150}{10} = 15$
$V a r i a n c e = \frac{\sum (x - ¯ ¯ ¯ x)^{2}}{10}$
$= \frac{(6 - 15)^{2} + (8 - 15)^{2} + (10 - 15)^{2} + (12 - 15)^{2} + (14 - 15)^{2} + (16 - 15)^{2} + (18 - 15)^{2} + (20 - 15)^{2} + (22 - 15)^{2} + (24 - 15)^{2}}{10}$

$= \frac{(- 9)^{2} + (- 7)^{2} + (- 5)^{2} + (- 3)^{2} + (- 1)^{2} + (1)^{2} + (3)^{2} + (5)^{2} + (7)^{2} + (9)^{2}}{10}$

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

$= \frac{330}{10}$
$= 33$

$∴$ Variance $= 33$

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6, 8, 10, 12, 14, 16, 18, 20, 22, 24

$x_{i}$	$10$	$15$	$18$	$20$	$25$
$f_{i}$	$3$	$2$	$5$	$8$	$2$

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
frequency	$6$	$5$	$8$	$15$	$7$	$6$	$3$

15, 20, 22, 25, 30, 20, 15, 20, 12, 20

Marks (x)	$0 \leq x < 10$	$10 \leq x < 20$	$20 \leq x < 30$	$30 \leq x < 40$	$40 \leq x < 50$
Frequency (f)	6	16	24	25	17

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