Calculate standard deviation from the following data using step d… - Vidyadip

Question

Calculate standard deviation from the following data using step deviation method:

Marks:	0-10	10-20	20-30	30-40	40-50
No. of Students:	4	3	6	4	2

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Answer

Marks	No. of Students (f)	M.V. (X)	$dx$	$dx'$	$dx'^2$	$fdx'$	$fdx'^2$
0-10	4	5	-20	-2	4	-8	16
10-20	3	15	-10	-1	1	-3	3
20-30	6	25	0	0	0	0	0
30-40	4	35	10	1	1	4	4
40-50	2	45	20	2	4	4	8
	$\Sigma\text{f}=19$					$\Sigma\text{fdx}'=-3$	$\Sigma\text{fdx}'^2=31$

S.D. $=\sqrt{\frac{\Sigma\text{fdx}'^2}{\Sigma\text{f}}-\Big(\frac{\Sigma\text{fdx}'}{\Sigma\text{f}}\Big)^2}\times\text{i}$
$=\sqrt{\frac{31}{19}-\Big(\frac{-3}{19}\Big)^2\times10}$
$=\sqrt{1.63-.03}\times10=\sqrt{1.60}\times10$
$=1.26\times10=12.6$

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