Variance Calculator
Calculate the variance of your data set to understand its spread and dispersion.
Enter Your Data
Table of Contents
Variance Formula
Variance is a measure of the spread between numbers in a data set. It measures how far each number in the set is from the mean and thus from every other number in the set.
Where:
- s² is the variance
- Σ is the sum of
- x is each value in the data set
- μ is the mean of the data set
- n is the number of values
How to Calculate Variance
To calculate variance, follow these steps:
-
1Calculate the mean (average) of the data set
-
2Subtract the mean from each value and square the result
-
3Calculate the mean of these squared differences
Interpreting Variance
Understanding what the variance tells you about your data:
-
1Small Variance:
Indicates that the data points are close to the mean, showing little variation.
-
2Large Variance:
Indicates that the data points are spread out over a wider range of values.
-
3Zero Variance:
Indicates that all values in the data set are identical.
Practical Examples
Example 1 Test Scores
A class of students has test scores: 85, 87, 89, 91, 93
Mean = 89
Variance = 10
This small variance indicates that the scores are clustered close to the mean.
Example 2 Stock Prices
Daily stock prices over a week: $100, $120, $90, $130, $110
Mean = $110
Variance = 250
This larger variance shows significant price volatility.
Example 3 Temperature Readings
Daily temperatures: 20°C, 20°C, 20°C, 20°C, 20°C
Mean = 20°C
Variance = 0
Zero variance indicates constant temperature.