# Variance calculator

## The step-by-step instructions to calculate variance using the formula:

1. Find the mean (average) of the set of numbers by adding up all the numbers in the set and dividing by the total number of values.
2. For each number in the set, subtract the mean from the number.
3. Square each of the differences obtained in step 2.
4. Add up all of the squared differences obtained in step 3.
5. Divide the sum obtained in step 4 by the total number of values in the set minus 1. This is the variance.

## Variance formula

The formula for variance is:

σ² = Σ(x – μ)² / N

Where:

• σ² = variance
• Σ = sum of
• x = each value in the set
• μ = the mean (average) of the set
• N = the total number of values in the set

### To calculate the variance using this formula, follow these steps:

1. Find the mean (average) of the set of numbers by adding up all the numbers in the set and dividing by the total number of values.
2. For each number in the set, subtract the mean from the number.
3. Square each of the differences obtained in step 2.
4. Add up all of the squared differences obtained in step 3.
5. Divide the sum obtained in step 4 by the total number of values in the set minus 1. This is the variance.

The variance is a measure of how spread out the data is from the mean. It is commonly used in statistics and probability theory to quantify the variability or dispersion of a set of data.

To illustrate this formula with an example, let’s say we have the following set of numbers: 4, 7, 11, 14, 20.

1. Find the mean:
• Add up all the numbers: 4 + 7 + 11 + 14 + 20 = 56
• Divide by the total number of values: 56 ÷ 5 = 11.2
• The mean is 11.2.
2. Subtract the mean from each number:
• 4 – 11.2 = -7.2
• 7 – 11.2 = -4.2
• 11 – 11.2 = -0.2
• 14 – 11.2 = 2.8
• 20 – 11.2 = 8.8
3. Square each of the differences:
• (-7.2)² = 51.84
• (-4.2)² = 17.64
• (-0.2)² = 0.04
• 2.8² = 7.84
• 8.8² = 77.44
4. Add up all the squared differences:
• 51.84 + 17.64 + 0.04 + 7.84 + 77.44 = 154.80
5. Divide by the total number of values minus 1:
• 154.80 ÷ (5 – 1) = 38.70
• The variance of the set is 38.70.

Therefore, the variance of the set {4, 7, 11, 14, 20} is 38.70.