Deck 4: The Normal Distribution

Question 1

In statistics, the word "distribution" comes up a lot. In your own words, first tell me what a distribution is. Then, again in your own words, explain what a "normal distribution" is.

Answer 1

A distribution is any collection of scores, arranged from the smallest score to the largest. In a frequency distribution, we usually use a graph with a Y axis and an X axis. On the Y axis is the frequency, or how often a score in the distribution occurs. The X axis has the value of the scores. In a normal distribution, the scores that occur most often are in the middle, and the frequencies of the scores drop lower and lower the further you move away from the middle on either side. This produces a bell-shaped graph.

Question 2

What does "asymptotic" mean and why is it important?

Answer 2

It means that the ends of the normal distribution never cross the X axis. That is important because it means that it is always possible to get extreme scores by chance. It may not be likely, but it is possible.

Question 3

In statistics, we use the normal distribution a lot. What is so great about it? In other words, what does it do for us? Tell me something that the normal distribution lets us, as statisticians, do that we cannot do without it.

Answer 3

We love the normal distribution because it allows us to determine the probabilities of events occurring by chance. If I know that a variable has a normal distribution (e.g., height, weight, scores on a test, number of shirts owned, etc.) I can figure out the probability of randomly selecting an individual who is a certain height, weight, with a certain score on a test, etc. This is very useful information.