Baking With Math: Bootstrapping

Bootstrapping is an option you take when the data in hand is kind of shitty, so you shuffle it, and resample it to clone more data, and pray that the clone represents reality (the population).

Standard deviation, if you recall from our Baking With Math series, is a measure of how well mixed your batter, which represents, portentously, reality, is. If you take a bunch of spoonful's of your batter, in other words, the mean mixed-upness of those spoonfuls is fairly likely to represent how mixed up the data is in the population. You could get one spoonful that is mostly egg vs not-egg, and get one spoonful that is mostly sugar vs not-sugar, and still your mixed-upness gauge could still be accurate with respect to the overall population.

Mean, on the other hand, converges to a center, and as such, is more susceptible to spikes in the gauge. If your spoonfuls contain even one outlier of mixed-upness, your sense of the typical nature of that batter, the centeredness of the population, is going to be way off. A spoonful of egg in no way represents the batter, and its inclusion in an already shitty data set is going to have major implications for your ability to form beliefs about reality.