 There are three basic types of averages on the SAT that you should be pretty comfortable with at this point, and all of them start with the letter “m.” Those are the mean, the median, and the mode. In case those aren’t second nature, let’s define them, quickly.

Mean

This is the most commonly used type of average and the most commonly tested on the SAT. The formula is simple enough. where n is the number of terms added in the numerator.  In the set of numbers {2,3,4,5}, 3.5 would be the mean, because 2+3+4+5=14, and Median

If the numbers in a set are listed in order, the median is the middle number. In the set {1,5,130}, 5 is the median. In the set above, {2,3,4,5}, the median is 3.5, which is the mean of the middle two terms since there’s an odd number of them.

Mode

The mode is just the number that shows up the most often. It’s perfectly possible that there is no mode or that there are several modes. In the set {5,7,7,9,18,18}, both 7 and 18 are modes.

What’s important to know about averages on the SAT

Averages come up in an algebra or word problems. You’ll usually have to find some value using the formula for a mean, but it may not be as simple as finding the average of a few numbers.  Instead, you’ll have to plug some numbers into the formula and then use a bit of algebra or logic to get at what’s missing.

For example, you might see a question like this:

If the arithmetic mean of x, 2x, and 6x is 126, what is the value of x?

To solve the question, you’ll need to plug it all in to the formula and then do some variable manipulation.   Medians and modes, on the other hand, don’t show up all that often. Definitely be sure that you can remember which is which, but expect questions on means, most of the time.

One more averages practice problem

If three sisters have an average (arithmetic mean) age of 24, and the youngest sister is 16, what is the sum of the ages of the two older sisters?

1. 28
2. 32
3. 56
4. 60
5. 72

If you’re careful to remember that the question is asking you for the sum of the sisters’ ages, you can solve this one pretty quickly. Keep in mind that we can’t find their individual ages, though. There’s not enough information for that. First we find the total combined age of the three, which must be 72, since . Careful not to fall for the trap that is (E), we take the last step and subtract 16 from that total age to find the leftover sum, which is 56, or (C).

Lucas is the teacher behind Magoosh TOEFL. He’s been teaching TOEFL preparation and more general English since 2009, and the SAT since 2008. Between his time at Bard College and teaching abroad, he has studied Japanese, Czech, and Korean. None of them come in handy, nowadays.

2 Responses to “SAT Math: Types of Averages”

1. M says:

Hi I was doing one of these problems listed above.
If the arithmetic mean of x, 2x, and 7x is 127, what is the value of x?
In the equation you have 126 instead of 127.
So x+2x+7x/3 = 126
x+2x+7x = 378
10x=378
x= 37.8 You could only get 42 if you divided by 9, right? I just want to know if I’m
doing it correctly. Thanks

2. Kristin Fracchia says:

Hi M! You are absolutely right! Thank you for catching our typo (embarrased face). We’ve fixed the problem in the post. Three cheers for your eagle eyes!

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