Variance calculator
Calculate sample or population variance from up to 12 values while ignoring blank fields.
What this calculator covers
Use this calculator when you want the squared-units spread measure directly instead of only the square-rooted standard deviation.
Keeping the variance and standard deviation together is useful when you need to compare formulas, check homework, or confirm a statistics workflow by hand.
Frequently asked questions
- When should I choose sample variance instead of population variance?
- Use sample variance when your data is a subset drawn from a larger group and you want to estimate the spread of the full population. Use population variance when your data represents every member of the group being described. Sample mode divides by n − 1 rather than n to correct for the underestimation that occurs with small samples.
- Why does variance use squared units?
- Squaring each deviation from the mean ensures that values above and below the mean both contribute positively to the spread measure, and it gives larger deviations more weight than smaller ones. The standard deviation undoes the squaring to return a spread figure in the original units.
- How many values can I enter?
- The calculator accepts up to 12 numeric values. Blank fields are ignored, and at least two non-blank values are required to compute a result.
- What is the relationship between variance and standard deviation?
- Standard deviation is the square root of variance. The calculator reports both so you can use whichever is more meaningful — variance for theoretical comparisons and standard deviation for communicating spread in the same units as the data.
Tool
Run the calculation
Result
RESULT · VARIANCE
â„–157
Primary result
23.5
For the 6-value set 8, 12, 12, 15, 19, 21, the sample variance is 23.5 and the matching standard deviation is 4.84768.
- Values used
- 8, 12, 12, 15, 19, 21
- Mean
- 14.5
- sample variance
- 23.5
- Supporting standard deviation
- 4.84768
Step-by-step solution
- 1.Find the mean 14.5 so each observation can be measured as a deviation from the center.
- 2.Square those deviations and divide by n - 1 to get the sample variance 23.5.
- 3.Take the square root when you want the supporting standard deviation 4.84768 in the original units.
Walkthrough
Visual walkthrough
Variance keeps the spread in squared units so large deviations weigh more heavily than small ones.
01
Measure every value from the mean
Mean = 14.5
The mean becomes the reference point for every squared deviation.
02
Average the squared deviations
sample divisor n - 1
Population mode divides by n. Sample mode divides by n - 1 to estimate spread from a sample.
03
Read the spread
Variance is the squared-units spread measure, while the standard deviation is its square root.
Variance 23.5 · SD 4.84768