We can use reducers in a lot of different situations, but sometimes we'll need to change how we process data to do so.
For this example, we'll show how to compute summary statistics with reducers. We'll use some algorithms and formulas first proposed by Tony F. Chan, Gene H. Golub, and Randall J. LeVeque in 1979 and later extended by Timothy B. Terriberry in 2007. These allow us to approximate mean, standard deviation, and skew for online data—that is, for streaming data that we may only see once—so we'll need to compute all the statistics on one pass without holding the full collection in memory.
The following formulae are a little complicated and difficult to read in lisp-notation. But there's a good overview of this process, with formulae, on the Wikipedia page for Algorithms for calculating variance (http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance). And to simplify this example somewhat, we'll only calculate the mean...