Statistics - Standard Deviation of Individual Data Series

Quiz

When data is given on individual basis. Following is an example of individual series:

Items	5	10	20	30	40	50	60	70

For individual series, the Standard Deviation can be calculated using the following formula.

Formula

$\sigma = \sqrt{\frac{\sum_{i=1}^n{(x-\bar x)^2}}{N-1}}$

Where −

Problem Statement:

Calculate Standard Deviation for the following individual data:

Items	14	36	45	70	105

Solution:

${X}$	${\bar x}$	${x- \bar x}$	${(x - \bar x)^2}$
14	54	-40	1600
36	54	-18	324
45	54	-9	81
70	54	16	256
105	54	51	2601
${N=5}$			${\sum{(x - \bar x)^2} = 4862}$

Based on the above mentioned formula, Standard Deviation $ \sigma $ will be:

$ {\sigma = \sqrt{\frac{\sum{(x - \bar x)^2}}{N-1}} \\[7pt] \, = \sqrt{\frac{4862}{4}} \\[7pt] \, = \sqrt{\frac{4862}{4}} \\[7pt] \, = 34.86}$

The Standard Deviation of the given numbers is 34.86.

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