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.
Continue ReadingThe 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.
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.
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.