# Dispersion and Variability (Standard Deviation)

The topics dispersion and variability (or variance) describes the “spread” of data in a distribution. This article explains how to compute the variance and the standard.

The first measure of dispersion to look at is the variance. Let’s look at the data set below:

 X Values 4 5 2 7

## Steps to Calculate Variance:

1. Calculate mean
2. Subtract each value in set from mean
3. Square each number from 2)
4. Sum the values from 3)
5. Divide by the number of values in the set

Let’s work through these steps. First, let’s calculate the mean:

M = ∑X / n (the sum of X divided by N)
M = 4 + 5 + 2 + 7 / 4
M = 18 / 4
M = 4.5

Second, we subtract each value in the set from the mean.

 X Values X – M 4 -0.5 5 0.5 2 2.5 7 2.5

Third, we square each value.

 X Values X – M (X – M)2 4 -0.5 0.25 5 0.5 0.25 2 -2.5 6.25 7 2.5 6.25

Forth, we sum the values from the third.

 X Values X – M (X – M)2 4 -0.5 0.25 5 0.5 0.25 2 -2.5 6.25 7 2.5 6.25 ∑ 13

Finally, we divide by the number of values in the set:

Variance is 13 / 4 = 3.25

To calculate the standard deviation, you simply take the square root of the variance.

Sqrt(3.25) = 1.80

So, the standard deviation is 1.80. You can confirm this by going into Excel and using the STDEV.P formula

Cite this article as: MacDonald, D.K., (2015), "Dispersion and Variability (Standard Deviation)," retrieved on December 14, 2019 from http://dustinkmacdonald.com/dispersion-and-variability-standard-deviation/.

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