How Numbers Can Fool You
by Laura Dolson
January 31, 2005
Reminder: Please bring your health articles to class!
Also, this week, don't do a summary, just answer the questions in red, and go to the Web site. I'm trying to shorten my articles and give you a little less work.
About 10 years ago, a professor was reading the introduction to the research of one of his students, who was working on her PhD. The first line read, "Every year since 1950, the number of American children gunned down has doubled"*.
Could this be true? Why or why not?
There are many ways that people can be misled. The most common one is probably just choosing the statistic that favors the writer's point of view. This temptation is hard to ignore - if you know that one way of describing the numbers will make the point you want to make, you are very likely to use that description. Our job as readers is to ask, "what other statistic are they not telling us that might answer the question better?"
Example #1: "Average" could be the mean or the median.
The "mean" is what we usually think of as average, where you add up all the numbers and divide by how many there are. Grades are usually determined this way. The "median" is simply the middle number in a bunch of number - half of the numbers will be greater than the median, and half will be less. Both of these can legitimately be called the "average".
Suppose you got the following grades in math over the course of a trimester:
68, 70, 72, 83, 100
72 is the median (middle number), and 79 is the mean. Which "average" would you rather tell your parents about?
Now, imagine that instead of getting that "100", you forget about the test, didn't study, and got a 30:
30, 68, 70, 72, 83
In this case, the mean would be 64.6, but the median is 72. Now, which average would you want to report to your parents?
In both cases, which do you think gives the best information about the math ability of someone who got those grades?
Example #2: Percentages vs Actual Numbers
Suppose you hear that eating watermelon pits doubles your chances of getting an ulcer (it doesn't!). But then you find out that across the country, only 4 people your age per year get ulcers in the first place! In this case, you really want to know the real numbers, not just the percentages. On the other hand, there are a lot of circumstances where the actual numbers are not as helpful. Knowing that 400 people in California got the flu this year, as opposed to only 200 in Iowa, doesn't tell give us much information about our own risk of getting the flu, unless we know the populations of California and Iowa. Percentages would be much more helpful in a case like this. Even more helpful is to know what percentages of flu victims were different ages.
Web sites of the Week:
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