Mean & Variance and the Right & Left

Both sides of the political spectrum use data to justify their opinions. In general, people on the ‘Left’ tend to focus on variance and people on the ‘Right’ tend to focus on mean. Statistical distributions — at the very least — have both mean and variance. That is, every statistical distribution has both a mean and a variance (and often other parameters as well).

The Right tends to focus on general macro trends (read: means; e.g., “group X is different than group Y”) and the Left tends to focus on exceptions to the rule (read: variance & outliers; e.g., “this general trend doesn’t hold because of this counterexample”).

Anyone familiar with statistics knows that mean and variance need to both be considered when looking at any statistical distribution. Sometimes this can seem paradoxical in practice. Consider some data that shows men and women are different along some axis/dimension (call it dimension D), with statistical significance. Also consider that the two distributions along that axis both have a large variance, resulting in a large overlap between distributions. (See the image at the top.)

In practice, this means that one can reasonably conclude that a group of men and a group of women will — in the aggregate — be different along dimension D. However, given a single woman and a single man, one wouldn’t be able to conclude (i.e. with statistical significance) that one of them is higher along dimension D. This very much feels like a paradox. Someone familiar with statistics can usually handle this paradox quite well, but the general public cannot. This results in a lot of painful political debates — blind men touching different parts of an elephant.