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charting:tableau:functions:standard-deviation-of-a-population

## Standard Deviation of a Population

The standard deviation is a measure of the spread of scores within a set of data. The symbol used for, is called sigma σ. We are normally interested in knowing the population standard deviation because our population contains all the values we are interested in. There are two standard deviations: The sample standard deviation and the population standard deviation. Data, in statistics, is often presented by a sample only. But it is possible to estimate the population standard deviation from a sample standard deviation. 1)

To get the standard deviation first get the variance. The variance is defined as the average of the squared differences from the mean. The mean is the simple average of the numbers. Then for each number: Subtract the Mean and square the result 2)

#### Example

The heights of this children are: 75 cm, 60 cm, 105 cm and 135 cm. Mean = (75 + 60 + 105 + 135) / 4 = 375 / 4 = 93,75

Afterwards we calculate the difference from the Mean: 4) To calculate the Variance, each difference is taken and squared and then the result has to be averaged.

Variance σ²: [ (-18,75)² + (-33,75)² + 11,25² + 41,25² ] / 4 = 653,90

And the Standard Deviation is just the square root of Variance:

Standard Deviation σ: √653,90 = 25,57

Our example was for a Population (the four children we are interested in). But if the data is a Sample (a selection taken from a bigger Population), then the calculation changes: Divide by N-1 when calculating Variance

#### Formulas

2)
MathisFun – Standard Deviation and Variance - Stand 02.06.2016 https://www.mathsisfun.com/data/standard-deviation.html/
3) , 4) , 5)
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