The variance in probability theory and statistics is a way to measure how far a set of numbers is spread out. Variance describes how much a random variable differs from its expected value. The variance is defined as the average of the squares of the differences between the individual (observed) and the expected value. That means it is always positive. In practice, it is a measure of how much something changes. For example, temperature has more variance in Moscow than in Hawaii.
The variance is not simply the average difference from the expected value. The standard deviation, which is the square root of the variance and comes closer to the average difference, also is not simply the average difference. Variance and standard deviation are used because it makes the mathematics easier when adding two random variables together.
- "Standard Deviation and Variance," Maths Is Fun