It seems like taking the mean of a sample is not controversial. However, it could be the wrong thing to do. Consider this neat example from
D. J. Hand, “Deconstructing statistical questions,” J. Royal Statistical Society A (Statistics in Society), vol. 157, no. 3, pp. 317-356, 1994.
An English researcher and French researcher both test two cars of two types to determine which type is the more fuel efficient. One researcher measures miles per gallon, and the other gallons per mile. The following data are collected:
The English researcher finds the average miles per gallon of type 1 cars is greater than that of type 2, so they conclude type 1 is more fuel efficient. However, the French researcher finds the average gallons per mile of type 2 cars is less than that of type 1, so they conclude type 2 is more fuel efficient.
Who is right??