Sample Variance Calculator

Sample variance is the measure of variation seen in the sample data in a single sample. In calculating terms it can be explained as the average of the squared differences from the Mean. As the definition states, we have 3 steps to calculate it.

Step 1: Calculate the mean of the sample data.
Step 2: Subtract the mean from the original value for each sample data and square the result.
Step 3: Add all the output from step 2 and divide it with N-1.

Sample Variance Calculation

Result:

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Formula: Sample Variance Formula Where, σ = Sample Variance X = Input Value μ = Mean N = Number of Scores

Example

Sample Variance

Lets consider x value 4,8,2,9.
Find the mean value to get sample varians σ2
μ = (4 + 8 + 2 + 9) / 4
μ = 5.75

Find th sum of difference of sample data to the mean and square the obtained value (x - μ)2
4 = 3.0625
8 = 5.0625
2 = 14.0625
9 = 10.5625
∑(x - μ)2 = 3.0625 + 5.0625 + 14.0625 + 10.5625
∑(x - μ)2 = 32.75

Then, dividing by the total value which is subtracted by 1 (N-1)
σ2 = 32.75 / (4 - 1)
σ2 = 10.9167

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