Variance Calculator
Enter a data set for a population or sample to calculate variance using the calculator below.
Results:
| Variance (σ²): | |
|---|---|
| Standard Deviation (σ): | |
| Sum of Squares (SS): | |
| Population Size (N): | |
| Mean (μ): |
Steps to Solve
Variance Formula
Step One: Find the Mean
Mean (μ) = sumpopulation size (N)
Step Two: Find the Sum of Squares
Sum of Squares (SS) = ∑(xi - μ)²
Step Three: Calculate the Variance
Variance (σ²) = SSN
| Variance (σ²): | |
|---|---|
| Standard Deviation (σ): | |
| Sum of Squares (SS): | |
| Population Size (N): | |
| Mean (μ): |
Steps to Solve
Variance Formula
Step One: Find the Mean
Mean (μ) = sumpopulation size (N)
Step Two: Find the Sum of Squares
Sum of Squares (SS) = ∑(xi - μ)²
Step Three: Calculate the Variance
Variance (σ²) = SSN
| Variance (s²): | |
|---|---|
| Standard Deviation (s): | |
| Sum of Squares (SS): | |
| Sample Size (n): | |
| Mean (x̄): |
Steps to Solve
Variance Formula for a Sample
Step One: Find the Mean
Mean (x̄) = sumsample size (n)
Step Two: Find the Sum of Squares
Sum of Squares (SS) = ∑(xi - x̄)²
Step Three: Calculate the Variance
Variance (s²) = SSn - 1
How to Find Variance
Variance is a statistical measure of the variability from the mean in a data set. It is essentially a way to measure the spread between numbers and their center in the data set.
The symbol for variance is σ², pronounced sigma-squared. Variance can also be used to measure variability in a sample data set, and in this case, it is represented as s².
Variance is often used to find the standard deviation, which is equal to its square root.
Variance Formula
You can use the following formula to find the variance.
There are three main components to the formula, and you can find the variance of a data set in a few simple steps.
Find the Mean
Because variance is a measurement of the variability from the mean, it makes sense that the first step to finding the variance is to calculate the mean of the data set.
To calculate the mean, simply sum each value in the data set, then divide the result by the number of elements in the set.
mean = sumcount
The mean formula looks more like this:
μ = (x1 + x2 + … + xi) ÷ N
μ = ∑xi ÷ N
Find the Sum of Squares
Once you have the mean, the next step is to calculate the sum of squares. You can use the following formula to calculate the sum of squares.
SS = ∑(xi – μ)²
The sum of squares SS is equal to the sum of each value xi minus the mean μ, squared.
Find the Variance
Finally, using the sum of squares, you can find the variance.
σ² = SSN
Thus, the variance σ² is equal to the sum of squares SS minus the number of elements in the data set N.
How to Find Sample Variance
You can use the formula above to calculate the variance for a data set that represents a population, but the formula to find the variance of a sample is slightly different.
The variance of a sample s² is equal to the sum of squares divided by the number of elements in the sample n minus 1.