The Normal Distribution and "The Bell Curve"

Student: What is the Bell Curve?

Mentor: The bell curve is another name for the normal distribution. The normal distribution is a common type of graph that has more or less the shape of a bell. "The Bell Curve" was also the title of a highly controversial book published back in 1994.

Student: What could be controversial about a graph?

Mentor: Well, the book wasn't really about the graph it was about intelligence. If you graph scores on an IQ test on the horizontal axis, and number of people who got that score on the vertical axis, then you get the bell curve shape. The authors were talking about the way intelligence was distributed among people, so...

Student: So they used the shape as the title of the book. But why is that controversial?

Mentor: The book was controversial because it suggested that whole races were more or less intelligent than others.

Student: That's racist! How can someone say if I'm smart or not because of the color of my skin?

Mentor: They can't. A lot of people thought that at the time though. About a year later, a number of scientists published evidence that the book was wrong. But you know what? Even if the book were right, it is still impossible to guess how smart you as an individual are, or compare your intelligence to another individual, based on your skin color. We can demonstrate this with mathematics.

Student: How? Show me.

Mentor: Well, first you'll need to know some things about the normal distribution and statistics in general.

Student: I remember mean and median from the Measures activity .

Mentor: Good. That will help. Do you remember mode?

Student: Yes. Mode is the most common value.

Mentor: There is one more number that you need to know for this, but it is one you don't see as much. The standard deviation tells you how spread out numbers are from the average.

Student: You say average. Which kind of average are you talking about? Mean, median, or mode?

Mentor: That's a good question. It is from the mean, but it happens that in the normal distribution, the mean, median, and mode are all the same.

Student: That isn't very useful. Is it? I saw a lot of distributions where they were very different and only a few where they were the same.

Mentor: It gets more common when you are taking many, many data points. If you have a thousand plants, the mean, median, and mode will often get very close to the same number, and it will start representing the plants better.

Student: A lot of plants will be medium-sized?

Mentor: Yes, and a few will be extremely big or small. We see a lot of distributions in science with a lump in the middle and long tails trailing out to either side. Height, weight, number of kernels on a corncob, intelligence... all these make the same shape. Can you think of some?

Student: Speed of cars on a highway? Time it takes Derby horses to finish?

Mentor: In all these graphs, the important numbers are the average -- whichever average you use -- and the standard deviation, which you can experiment with in the Normal Distribution Activity .