Statistics - Standard Deviation of Individual Data Series

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

Items510203040506070

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 −

  • ${x}$ = individual observation of variable.

  • ${\bar x}$ = Mean of all observations of the variable

  • ${N}$ = Number of observations

Example

Problem Statement:

Calculate Standard Deviation for the following individual data:

Items14364570105

Solution:

${X}$${\bar x}$${x- \bar x}$${(x - \bar x)^2}$
1454-401600
3654-18324
4554-981
705416256
10554512601
${N=5}$  ${\sum{(x - \bar x)^2} = 4862}$

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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