Suppose you want to compute the average rainfall in Massachusetts, but the only data you have is from official rain gauges are in Boston, Lawrence, Worcester and Pittsfield. Suppose 42.1 inches of rain fell in Boston, 40.5 inches of rain fell in Lawrence, 43 inches of rain fell in Worcester and 50 inches of rain fell in Pittsfield in a particular year. How can you figure out the average rainfall for the state?

  Getting Started

The gauges in Boston, Lawrence and Worcester are all in the Eastern half of the state while the gauge in Pittsfield is only one in the west, so the gauge in Pittsfield represents the rainfall in more of the state than any of the other three. So each of the readings has to be "weighted" depending on what fraction of the state it represents.

  Going Deeper

Where would you locate two rain gauges in Idaho in order to determine the average rainfall in that state? Justify your choice.

Communicated by A. Heinricher.