Statistics by Amateurs

According to Ray Fisman of Slate, "It's a sad statistical reality: Half of us are below average." Well, I regret to inform Fisman and the editors at Slate that this claim is emphatically not "reality." Recall that "average" is also known as the "mean," which is the value derived by dividing the sum of a set of quantities by the number of quantities in the set. The "median" is the numeric value separating the higher half of a sample, population, or a probability distribution, from the lower half. The "mode" is the value that occurs the most frequently in a data set or a probability distribution. Fisman is confusing the "average" with "median" in his assertion.

Source: Shor (2010)

Consider the average per capita incomes in the US and The Netherlands as depicted above. The distributions show that the average income in the US is $36,092, while the average income in The Netherlands is $32,972. In other words, the average income in the US is higher than in The Netherlands. However, the median income in the US is $22,960, while the median in The Netherlands is $28,032. In other words, workers in The Netherlands generally earn more than workers in the US. Finally, the mode or most common annual income in the US appears to be around $20,000, while the mode in The Netherlands is clearly higher at an amount above that of the US.

The error that Fisman makes in his assertion that "half of us are below average" is a banal misconception, and demonstrates why analytical "amateurs" (in every field of endeavor) should take greater care with their use and interpretation of statistics.

Sources:

Fisman, R (2010, April 23), Nudges Gone Wrong, Slate.

Shor, D (2010, January 16), A Quick Trick for Approximating Median Income, Stochastic Democracy.

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The Flaw of Averages