SAT Math Types of Averages

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 â€Å"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,, 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? 28 32 56 60 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).