A simple math lesson for Donald Trump Jr.

Behind the numbers, with
Donald Trump Jr.
Behind the numbers, with Donald Trump Jr.
Image: Reuters/Nick Didlick
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Hey Don Jr.,

Just writing because I noticed a comment you made that suggests you are having a hard time with the concepts mean and median. You said:

Your comment was in response to this dopey headline about ACT scores:

The thing is, you don’t really need to “imagine” anything—after all, it’s math! So yeah, the thing is, it’s not true that “50% are below average” is “how math works.”

Let’s look at a simple example

Let’s say there are five people. They have 0, 1, 2, 3, and 100 apples, respectively. (That one guy must be quite the applepreneur!) In that setup, the average is 21.2. All four of the people with fewer than 100 apples would be below average, meaning 80% of the total sample! The correct word for what you are describing is not “average,” but “median.”

You are onto something, though

When data, like a set of numbers, is what we call “normally distributed,” then 50% of the sample is below average. And a lot of things in the world are more or less normally distributed, like height or—you guessed it—test scores. Even in the case of something like that, though, the distribution won’t be perfectly normal, so in reality the proportion of people below the mean will probably not be exactly 50%.

For example, look at scores for AP tests (pdf), given to high-achieving American high schoolers. In 2016, the average score for the computer science test was 3.04, but 58.7% of test-takers got a three or below (out of five). So close to 60% were below average.

Hope that helps!