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:
- Calculate mean
- Subtract each value in set from mean
- Square each number from 2)
- Sum the values from 3)
- 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
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