# Fallacy of averages

### From Glossary

Imagine standing with one foot on a keg of ice and the other in a fire. Your average
body temperature may be fine, but the extremes will kill you! The
*fallacy of averages* is the fallacious results you may get
when replacing data with their expected values. Formally, the
fallacy is stated as –
viz., the covariance is not zero. Another form of this fallacy is
that (unless is linear). In
particular, suppose we have

where is a vector of parameters with some uncertainty. The fallacy of averages suggests that it is a mistake to replace with its expected value for at least 2 reasons: (1) members of may be correlated, and (2) the average values of and need not equal the functional values at the mean.