Comment by kqr
4 years ago
The other common misuse of averages I keep hearing confusing "the average X" with "the X of the average Y". (Known formally as Jensen's inequality.)
So for example, the average time to review a code change is not the same as the time it takes to review a code change of average size.
The average user experience of a website is not given by the user experience of the average response time.
And so on. People tend to compute the average of an easier variable and then forget that the derived value of interest is often nonlinear in the easier variable.
Nit: Jensen's inequality only applies when the "derived value of interest" is a convex function of the "easier variable".
very interesting. what is the suggested correct way then?
Draw a random sample of easy variables from the underlying distribution, compute the variable of interest on all of those, then average.