The S.D. of the following freq. dist.
Class 0-10 10-20 20-30 30-40
$f_{i}$ 1 3 4 2

7.8

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9

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8.1

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0.9

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Solution

The correct option is C $9$
Class $x_{i}$ $f_{i}$ $u_{i} = \frac{x_{i} - A}{h}$ $u_{i}^{2}$ $f_{i} u_{i}$ $f_{i} u_{i}^{2}$
0-10 5 1 -2 4 -2 4
10-20 15 3 -1 1 -3 3
20-30 25 4 0 0 0 0
30-40 35 2 1 1 2 2
Total 10 -3 9
$S . D .$ $= h \sqrt{\frac{\sum f_{i} u_{i}^{2}}{\sum f_{i}} - {(\frac{\sum f_{i} u_{i}}{\sum f_{i}})}^{2}}$
$S . D . = 10 \sqrt{\frac{9}{10} - {(\frac{- 3}{10})}^{2}} = 9$

Suggest Corrections

Class:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency:	18	16	15	12	10	5	2	1

Class interval:	0−10	10−20	20−30	30−40	40−50
Frequency:	9	12	15	10	14

Class interval:	0−10	10−20	20−30	30−40	40−50	50−60	Total
Frequency:	5	f₁	20	15	f₂	5	60