The table above lists the results of a survey of a random sample of 250 high school seniors and freshmen. Each student selected one subject that was his or her favorite.If the sample is representative of a high school with 2,000 freshmen and seniors, then based on the table, what is the predicted number of freshmen at the high school who would select math as their favorite high school subject? A) 520 B) 240 C) 65 D) 30

If the survey is of a true random sample, then you would expect the proportion of freshmen who like math in the sample to be pretty close to the proportion of freshmen who like math in the whole school’s population. \dfrac{30}{130}=\dfrac{3}{13} of freshmen chose math as their favorite subject, so roughly 3/13 of the freshman population probably feels the same way.

In my opinion, this question is trying to get a little too cute by using freshmen and seniors (instead of just including all grades). I don’t think a real question would do that. But what the question is getting at when it says that there are 250 total in the sample and 2000 freshmen and seniors overall is that you can just multiply every number by 8 and have a decent approximation of the preferences of the full population because \dfrac{250}{2000}=\dfrac{1}{8}.

So, just multiply! 8\times 30=240, so the answer is B.

Comments (5)

Thanks for the explanation – your way was definitely easier than the way I did it. FYI – This was from the 2015 PSAT (so it’s definitely ‘real’).

Thanks again.

I wish I had noticed that it wasn’t just 30 freshmen choosing math out of 130 total freshmen surveyed, but 30 freshmen choosing math out of 250 students (freshmen + seniors) surveyed. Then I could have set up a simple ratio of 30 to 250 = x to 2000.

I agree that the wording leaves much to be desired!

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