Find the standard deviation from the given data, using step devia… - Vidyadip

Question

Find the standard deviation from the given data, using step deviation method.

X	7.5	17.5	27.5	37.5	47.5
Frequency	10	8	15	6	4

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Answer

Calculation of Standard Deviation

X	Frequency (f)	$\text{d}'\Big(\frac{\text{X}-\text{A}}{\text{c}}\Big)\text{A}=27.5,\text{c = 10}$	fd'	$fd'^2$
7.5	10	-2	-20	40
17.5	8	-1	-8	8
27.5	15	0	0	0
37.5	6	1	6	6
47.5	4	2	8	16
	$\Sigma\text{f}=43$		$\Sigma\text{fd}'=-14$	$\Sigma\text{fd}'^2=70$

$\sigma=\sqrt{\frac{\Sigma\text{fd}'^2}{\Sigma\text{f}}-\Big(\frac{\Sigma\text{fd}'}{\Sigma\text{f}}\Big)^2}\times\text{c}$
$=\sqrt{\frac{70}{43}-\Big(\frac{-14}{43}\Big)^2}\times10$
$=\sqrt{1.63-0.106}\times10=\sqrt{1.524}\times10$
$\therefore\sigma=1.23\times10=12.3$

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