Variance Calculator

Enter numbers separated by commas to compute the population variance.

Step-by-step method

1. List the numbers and calculate the mean (μ).
2. Find each deviation from the mean (x − μ).
3. Square each deviation.
4. Average the squared deviations to get the population variance.

Formula:

Example 1: 3, 1, 4, 2

Step 1 - List the numbers and calculate the mean (μ).

In this problem: The numbers are 3, 1, 4, 2. The mean is μ = Σx ÷ n with n = 4.

Step 2 - Find each deviation from the mean (x − μ).

In this problem: Subtract the mean from each value: x − μ using μ = 2.5.

Step 3 - Square each deviation.

In this problem: Square each deviation to remove negatives.

Step 4 - Average the squared deviations to get the population variance.

In this problem: Add the squared deviations and divide by n = 4: σ² = Σ(x − μ)² ÷ n.

Final answer: Variance = 1.25

Example 2: 5, 6, 7, 8, 9

Step 1 - List the numbers and calculate the mean (μ).

In this problem: The numbers are 5, 6, 7, 8, 9. The mean is μ = Σx ÷ n with n = 5.

Step 2 - Find each deviation from the mean (x − μ).

In this problem: Subtract the mean from each value: x − μ using μ = 7.

Step 3 - Square each deviation.

In this problem: Square each deviation to remove negatives.

Step 4 - Average the squared deviations to get the population variance.

In this problem: Add the squared deviations and divide by n = 5: σ² = Σ(x − μ)² ÷ n.

Final answer: Variance = 2