Calculate the standard deviation for the following distribution.
Marks $(x)$ $10$ $20$ $30$ $40$ $50$
Number of students $(f)$ $4$ $3$ $6$ $5$ $2$

18.61

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24.61

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12.61

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None of these

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Solution

The correct option is C $12.61$

$x$

10

20

30

40

50

$f$

4

3

6

5

2

$¯ X = \frac{\sum f x}{\sum f} = \frac{40 + 60 + 120 + 180 + 200 + 100}{20} = 29$
Standard deviation $= \sqrt{\frac{\sum (x - ¯ X)^{2} f}{\sum f}}$
$= \sqrt{\frac{361 \times 4 + 81 (3) + 1 (16) + 12 (15) + 441 (2)}{20}}$
$= 12.609$
$\approx 12.61$

Suggest Corrections

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	5	10	20	40	30	20	10	4

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of stu.	$20$	$24$	$40$	$36$	$20$

X	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
f	$10$	$8$	$15$	$8$	$4$

Marks $(x)$	$10$	$20$	$30$	$40$	$50$
Number of students $(f)$	$4$	$3$	$6$	$5$	$2$