Averages on the Move

This note is concerned with how averages change when the items being averaged are transformed in a simple way. To make this more explicit we remind the reader of the definitions of four basic averages or means. Then we turn to a specific example, using the Celsius and Fahrenheit temperature scales to illustrate the problems involved. Denote the arithmetic mean, geometric mean, harmonic mean, and the root mean square by A, G, H, and R, respectively. For a set { a,, a2,... , a,1 ) of positive real numbers these four means may be defined by the equations