By its very definition, variance cannot be negative. Variance is the measure of how spread out a distribution is, and distance can never be negative. Additionally, the formula for variance ensures that its result cannot be negative.
- Determine the mean of a set of numbers
The mean of a data set is the average. The formula is x_bar = sum(x_i) / N, where N is the number of data points. However, if the data set is taken from a sample rather than a population, the number of data points is N - 1.
- Find the squared differences
For each number in the data set, subtract the mean, and square the result. Add all the results together. The formula is sum(x_i - x_bar)^2. Even if the result from subtracting the mean from the data point is negative, the fact that it is squared ensures the variance cannot be negative.
- Find the average of squared differences
To find the variance, divide the sum of the squared differences by N. The variance formula is sigma^2 = sum(x_i - x_bar)^2 / N. The mean cannot be negative, and the lowest possible value is 0. If N - 1 is zero, then the variance is undefined.