# Identifying outliers and unexpected values in bivariate relationships

A value might be unexpected, even if it is not an extreme value, when it does not deviate significantly from the distribution mean. Some values for a variable are unexpected when a second variable has certain values. This is easy to illustrate when one variable is categorical and the other is continuous.

The following diagram illustrates the number of bird sightings per day over a several year period, but shows different distributions for each of the two sites. One site has a mean sightings per day of 33, and the other 52. (This is fictional data.) The overall mean (not shown) is 42. What should we make of a value of 58 for daily sightings? Is that an outlier? That clearly depends on which of the two sites was being observed. If there were 58 sightings on a day at site A, 58 would be an unusually high number. Not so for site B, where 58 sightings would not be very different from the mean for that site: