Variance Calculator

This Variance Calculator helps you find the population variance of a list of numbers and shows each step clearly. It works by finding the mean, calculating the squared difference of each value from the mean, and then averaging those squared differences. This makes it useful for checking answers, understanding how variance is calculated, and practising statistics step by step.

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