A Field Guide to Lies: Critical Thinking in the Information Age Read Free Page B

careful of averages and how they’re applied. One way that they can fool you is if the average combines samples from disparate populations. This can lead to absurd observations such as:
On average, humans have one testicle.
    This example illustrates the difference between mean, median, and mode. Because there are slightly more women than men in the world, the median and mode are both zero, while the mean is close to one (perhaps 0.98 or so).
    Also be careful to remember that the average doesn’t tell you anything about the range. The average annual temperature in Death Valley, California, is a comfortable 77 degrees F (25 degrees C). But the range can kill you, withtemperatures ranging from 15 degrees to 134 degrees on record.
    Or . . . I could tell you that the average wealth of a hundred people in a room is a whopping $350 million. You might think this is the place to unleash a hundred of your best salespeople. But the room could have Mark Zuckerberg (net worth $35 billion) and ninety-nine people who are indigent. The average can smear across differences that are important.
    Another thing to watch out for in averages is the bimodal distribution. Remember, the mode is the value that occurs most often. In many biological, physical, and social datasets, the distribution has two or more peaks—that is, two or more values that appear more than the others.

    For example, a graph like this might showthe amount of money spent on lunches in a week (x-axis) and how many people spent that amount (y-axis). Imagine that you’ve got two different groups of people in your survey, children (left hump—they’re buying school lunches) and business executives (right hump—they’re going to fancy restaurants). The mean and median here could be a number somewhere right between the two, and would not tell us very much about what’s really going on—in fact, the mean and median in many cases are amounts that nobody spends. A graph like this is often a clue that there is heterogeneity in your sample, or that you are comparing apples and oranges. Better here is to report that it’s a bimodal distribution and report the two modes. Better yet, subdivide the group into two groups and provide statistics for each.
    But be careful drawing conclusions about individuals and groups based on averages. The pitfalls here are so common that they have names: the ecological fallacy and the exception fallacy. The ecological fallacy occurs when we make inferences about an individual based on aggregate data (such as a group mean), and the exception fallacy occurs when we make inferences about a group based on knowledge of a few exceptional individuals.
    For example, imagine two small towns, each with only one hundred people. Town A has ninety-nine people earning $80,000 a year, and one super-wealthy person who struck oil on her property, earning $5,000,000 a year. Town B has fifty people earning $100,000 a year and fifty people earning $140,000. The mean income of Town A is $129,200 and the mean income of Town B is $120,000. Although Town A has a higher mean income, in ninety-nine out of one hundred cases, any individual you select randomly from Town B will have a higher income than an individual selected randomly from Town A. The ecological fallacy is thinking that if you select someone at random from the group with the higher mean, that individual is likely to have a higher income. The neat thing is, in the examples above, that it’s not just the mean that is higher in Town B but also the median and the mode. (It doesn’t always work out that way.)
    As another example, it has been suggested that wealthy individuals are more likely to vote Republican, but evidence shows that the wealthier states tend to vote Democratic. The wealth of those wealthier states may be skewed by a small percentage of super-wealthy individuals.During the 2004 U.S. presidential election, the Republican candidate, George W. Bush, won the fifteen poorest states, and the