Variance is always non-negative. It can be zero, but it can never be negative.
Here's why:
- Variance measures how spread out a set of data is. It's calculated by averaging the squared differences between each data point and the mean.
- Squaring the differences ensures that the result is always positive. Even if a data point is below the mean, the difference is squared, making it positive.
Example:
Imagine we have the following data: 2, 4, 6, 8.
- Mean: (2 + 4 + 6 + 8) / 4 = 5
- Variance: [(2-5)^2 + (4-5)^2 + (6-5)^2 + (8-5)^2] / 4 = 5
As you can see, even though some data points are below the mean, the variance is still positive.
In summary: Variance is a measure of spread and is always non-negative.
