Math with Bad Drawings: Illuminating the Ideas That Shape Our Reality by Ben Orlin

Author:Ben Orlin [Orlin, Ben]
Language: eng
Format: azw3
Publisher: Running Press
Published: 2018-09-17T16:00:00+00:00

3. THE MODE

How It Works: It’s the most common value, the hippest, most fashionable data point.

What if each value is unique, with no repetitions? In that case, you can group the data into categories, and call the most common one “the modal category.”

When to Use It: The mode shines in conducting polls and in tabulating nonnumerical data. If you want to summarize people’s favorite colors, you can’t very well “total the colors up” to compute a mean. Or, if you’re running an election, you’ll drive citizens mad if you line up the votes from “most liberal” to “most conservative” and award the office to the recipient of the median ballot.

Why Not to Trust It: The median ignores the total. The mean ignores its allocation. And the mode? Well, it ignores the total, its allocation, and just about everything else.

The mode seeks a single most common value. But “common” does not mean “representative.” The modal salary in the United States is zero—not because most Americans are broke and jobless, but because wage earners are spread across a spectrum from $1 to $100 million, whereas all wageless people share the same number. The statistic doesn’t illuminate anything about the US. It’s true in virtually every country, an artifact of how money works.

Turning to “modal categories” can only partway solve the problem. It places a surprising power in the hands of the person presenting the data, who can gerrymander the category boundaries to suit their agenda. Depending on how I draw the lines, I can claim that the modal household in the US earns $10,000 to $20,000 (going by increments of 10,000), or $20,000 to $40,000 (going by increments of 20,000), or $38,000 to $92,000 (going by tax brackets).

Same data set, same statistic. And yet the portrait changes completely, depending on the artist’s choice of frame.

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