Variance calculator
The step-by-step instructions to calculate variance using the formula:
- 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.
- For each number in the set, subtract the mean from the number.
- Square each of the differences obtained in step 2.
- Add up all of the squared differences obtained in step 3.
- 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:
- 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.
- For each number in the set, subtract the mean from the number.
- Square each of the differences obtained in step 2.
- Add up all of the squared differences obtained in step 3.
- 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.
- 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.
- 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
- 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
- Add up all the squared differences:
- 51.84 + 17.64 + 0.04 + 7.84 + 77.44 = 154.80
- 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.