Identifying outliers with one variable

The concept of an outlier is somewhat subjective but is closely tied to the properties of a particular distribution; to its central tendency, spread, and shape. We make assumptions about whether a value is expected or unexpected based on how likely we are to get that value given the variable's distribution. We are more inclined to view a value as an outlier if it is multiple standard deviations away from the mean and it is from a distribution that is approximately normal; one that is symmetrical (has low skew) and has relatively skinny tails (low kurtosis).

This becomes clear if we imagine trying to identify outliers from a uniform distribution. There is no central tendency and there are no tails. Each value is equally likely. If, for example, Covid cases per country were uniformly distributed, with a minimum of 1 and a maximum of 10,000,000, neither 1 nor 10,000,000 would be considered an outlier.

We need to understand how a variable...