How to Calculate the Statistical Sample Variance

Calculating variance is important in statistical analyses.

Statistical sample variance is used to show how far values in a distribution fall from the mean. Calculating variance is used heavily in statistics, as you need to know the variance before you can calculate the standard deviation (the square root of the variance). Knowing the variance and standard deviation allows you to assess whether an individual datum point (e.g., a single test score) is normal (average), above average or below average.

Instructions

1. Calculate the mean by adding up all the numbers (e.g., individual scores) in a data set and dividing them by the number of data points (e.g., students who took the test). For example, if you have four students in your class who scored 100 points, 60 points, 70 points and 90 points on a test, the mean test score would be (100 + 60 + 70 + 90) / 4 = 80.

2. Subtract the mean from each individual datum point to find the difference. In our example, the differences would be 20, -20, -10 and 10, since 100 - 80 = 20, 60 - 80 = -20, 70 - 80 = -10 and 90 - 80 = 10.

3. Square each of these differences. In our example, the squared differences are 400, 400, 100 and 100.

4. Add these squared values together: 400 + 400 + 100 + 100 = 1000.

5. Divide the sum of the squared values by the number of data points to obtain the variance. In our example, the variance is 250, since 1000 / 4 = 250.

References

• Math Is Fun: Standard Deviation and Variance