media geométrica

¡Eh! ¡Atención a la media geométrica!

El insomnio y la serendipia me han hecho transitar por unas líneas en las que se lee: A plausible guess is to use their arithmetic mean, which is roughly 150 people per square mile. However, the right method is the geometric mean: $$ \text{best guess} = \sqrt{\text{lower endpoint} \times \text{upper endpoint}}.$$ The geometric mean is the midpoint of the lower and upper bounds—but on a ratio or logarithmic scale, which is the scale built into our mental hardware.