The geometric mean is very useful when dealing with percent growth. For example, if your population grows by 20 percent in the first tick, 50 percent in the next tick, and 30 percent in the third tick, you must take the geometric mean of 1.20, 1.50, and 1.30 to determine the average percent increase. The geometric mean of a list of n numbers is the n th root of the product of those numbers.
(a) Use REDUCE, *, and ^ to define a GEOMETRIC-MEAN reporter.
(b) One potential problem with the simple definition of geometric mean is that any 0s in the input list will cause the output to be 0. Often, we ' d rather just ignore 0s. Using FILTER, modify your procedure in (a) to ignore 0s.