An extrapolation is a way to "spread" a small sample over a large population. An extrapolation is a proportion that compares known data to unknown data. If 5 of 20 students admit to eating Froot Loops for breakfast, then unknown of 150 is possible to extrapolate.

Your class is probably an excellent example of a population. Most classes are a well mixed group of students that proportionally represent their school as a whole. Only one of the following would be a good sample of 6^th graders in our school.

Now let's extrapolate some data. You poll your classmates and find that 7 of 24 choose blue as their favorite color. To extrapolate that data over the entire 6^th grade you simply create the proportion 7 is to 24 as n is to 145. What does the 145 represent?

If 7 out of the 24 students polled choose blue as their favorite color, how many sixth graders in the school would choose blue?
Solve: 7 is to 24 as n is to 145.

So you would expect about 42 students to choose blue as their favorite color if you polled every sixth grader in the school. Let's poll every sixth grader in the county!
Solve: 7 is to 24 as n is to 1544.

There are many famous polls that you see on TV; The Gallup Poll, Pew Poll, FOX News/Opinion Dynamics Poll, etc.. These polls ask about 1000 people what they think, then extrapolate the data over the 280 million Americans.

A recent FOX News/Opinion Dynamics Poll asked 900 Americans the following question.
"Do you think burning the American flag should be legal or illegal?"
189 respondents said that people should be allowed to burn the US Flag if they want to. If you extrapolate that data over 280 million people, about how many Americans think you should be allowed to burn our flag?

58 million 800 thousand sure sounds like a lot of folks think flag burning is ok. The truth is that it is really a very small number (21%) and over 70% think people should go to jail for burning the flag. Extrapolations are very handy but you must be careful to look at the whole picture - and not get confused by large numbers. Which of the following best describes American opinion concerning flag burning?