Calling Bullshit: The Art of Skepticism in a Data-Driven World

by Carl T. Bergstrom

In these examples, we are observing a population with a range of values—a range of heights, for instance—and then summarizing that information with a single number that we call a summary statistic. For example, when describing the tall Dutch, we reported a mean height. Summary statistics can be a nice way to condense information, but if you choose an inappropriate summary statistic you can easily mislead your audience. Politicians use this trick when they propose a tax cut that will save the richest 1 percent of the population hundreds of thousands of dollars but offer no tax reduction whatsoever to the rest of us. Taking a mean of the tax cuts, they report that their tax plan will save families an average $4,000 per year. Maybe so, but the average family—if by that we mean one in the middle of the income range—will save nothing. The majority of us would be better off knowing the tax cut for a family with the median income. The median is the “middle” income: Half of US families earn more and half earn less. In this particular case, the median family would get no tax cut at all, because the tax cut benefits only the top 1 percent.