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Statistics - Standard Deviation of Individual Data Series
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 −
${x}$ = 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:
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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