Exercise

Harmonic mean

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the data. That is

$$ \text{harmonic_mean}(x) = 1 / \text{arithmetic_mean}(1 / x) $$

The harmonic mean is often used to average ratio data. You'll be using it on the price/earnings ratio of stocks in the Standard and Poor's 500 index, provided as std_and_poor500. Price/earnings ratio is a measure of how expensive a stock is.

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Look at std_and_poor500 (you'll need this later). Write a function, get_reciprocal, to get the reciprocal of an input x. Its only argument should be x, and it should return one over x.