Descriptive Statistics
Variance
Variance is calculated with the formula at the bottom of this page, but please don't memorize the formula. The idea of variance is too important to relegate to simple memorization. Let's understand it.
A histogram will allow us to visualize the distribution, but variance is a calculation that quantifies a certain aspect of the measure's distribution. The notion behind variance is how "spread out" or "inconsistent" the numbers are. Loosely speaking, if we have high variance then the numbers are "inconsistent" and "all over the place." On the other hand, if we have low variance then the numbers are "consistent" and "don't move around much." A variance of zero is possible; it would indicate all the measures are so highly consistent that they're completely equal to each another.
The figure below shows two histograms. One is the household income of product A's customers, and the other is the household income of product B's customers. The mean of household income is the same for both products, but the variance is much higher for product A than product B.
A brief English translation of the formula is this: Variance is the average squared distance from the mean.
A more detailed English translation is this: Consider the first observation in the data. Calculate the difference between the obvervation and the average of the observations. Call the result the observation's "distance from the mean." Next, square the distance from the mean. Call the result the observation's "squared distance from the mean." Next, calculate the same sort of squared difference from the mean for all the other observations. Calculate the sum total of all the squared differences from the mean. Divide the sum by the number of observations there were. The result is variance. When the observations are very different from one another (and, therefore, very different from the mean), the variance is high. When the observations are very similar to one another (and, therefore, very similar to the mean), the variance is low.