Find the standard deviation using the actual mean method. X 2 3 4… - Vidyadip

Question

Find the standard deviation using the actual mean method.

X	2	3	4	5	6	7
Frequency	2	3	9	21	11	5

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Answer

Calculation of Standard Deviation

X	Frequency(f)	fX	$\text{d}(\text{X}-\bar{\text{X}}),\bar{\text{X}}=5$	$d^2$	$fd^2$
2	2	4	-3	9	18
3	3	9	-2	4	12
4	9	36	-1	1	9
5	21	105	0	0	0
6	11	66	1	1	11
7	5	35	2	4	20
	$\Sigma\text{f}=51$	$\Sigma\text{f X}=255$			$\Sigma\text{fd}^2=70$

$\bar{\text{X}}=\frac{\Sigma\text{fX}}{\Sigma\text{f}}=\frac{255}{51}=5$
$\sigma=\sqrt{\frac{\Sigma\text{fd}^2}{\Sigma\text{f}}}=\sqrt{\frac{70}{51}}=\sqrt{1.37}$
$\sigma=1.17$

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