The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is

7

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9

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12

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14

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16

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Solution

The correct option is C $14$
Now, mean of given observation is
$¯ ¯ ¯ x = \frac{9 + 16 + 23 + 30 + 37 + 44 + 51}{7} = \frac{210}{7} = 30$
Therefore, standard deviation $= \sqrt{\frac{\sum (x_{i} - x)^{2}}{7}}$
$= \sqrt{\frac{(9 + 30)^{2} + (16 - 30)^{2} + (23 - 30)^{2} + (30 - 30)^{2} + (37 - 30)^{2} + (44 - 30)^{2} + (51 - 30)^{2}}{7}}$
$= \sqrt{\frac{(- 21)^{2} + (- 14)^{2} + (- 7)^{2} + (0)^{2} + (7)^{2} + (14)^{2} + (21)^{2}}{7}}$
$= \sqrt{\frac{441 + 196 + 49 + 49 + 196 + 441}{7}}$
$= \sqrt{\frac{1372}{7}}$
$= \sqrt{196} = 14$

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X	$10$	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$
f	$2$	$7$	$10$	$12$	$15$	$11$	$10$	$6$	$3$

Item	$8$	$10$	$12$	$14$	$16$	$18$
Frequency	$10$	$5$	$11$	$7$	$8$	$9$

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