# 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.