Tackling Mean, Median, and Mode on the SAT
Sometimes the SAT Math test gives you a group of numbers and asks you to find the average (or arithmetic mean), the median, or the mode.
This sort of problem is probably familiar to you if you’re into computing your grade-point average or your favorite baseball player’s batting average.
Finding the mean is easy: just add up the numbers and divide the total by the number of numbers you just added. For example, to find the average of 2, 4, and 9, add those three numbers (total = 15) and divide by 3. The average is 5.
The median is defined as the middle number in a list, when the list is in numerical order. If you have a list such as 5, 3, 8, 7, 2, and need to find the median, put the numbers in order: 2, 3, 5, 7, 8. The middle number, or median, is 5.
If you have an even number of numbers (say, 3, 5, 6, 7, 8, 10), the list has no middle number, so take the mean of the two numbers closest to the middle. In this example, the two numbers in question are 6 and 7, so the median is 6.5.
The mode is the easiest to find. In a mixed bag of numbers, the mode is the number or numbers that pop up most frequently. So if you have a set with two 4s and two 8s, plus a bunch of other single numbers, you have two modes, 4 and 8, in that set. You can also have a set with no mode at all if everything shows up the same number of times.
The following practice question asks you to first find the mean, median, and mode, and then compare them.
- Which of the following is true for the set of numbers 3, 4, 4, 5, 6, 8?
- A. mean > mode
- B. median > mean
- C. median = mode
- D. median = mean
The answer is Choice (A). If you average the terms, you get
which is the mean. The median is 4.5 (halfway between the third and fourth terms), and the mode is 4. So Choice (A) is the only one that fits.