When I first started reviewing previously administered ACT tests, I was pretty surprised to find just how often questions about mean (especially), median, mode, and range occurred. So much so, that I included these concepts in what I call ACT Math "Have to Know" in my books. Recently, I broke these terms down with an example problem in a YouTube video, but I explain below as well.
To first work with these terms, you have to have a number set (simply a list of numbers); oftentimes, number sets are given between brackets, like this:
{4, 6, 3, 3}
Students are sometimes intimidated by the brackets around the numbers, thinking they must refer to or require some kind of math knowledge they don't have. However, all it means is that this is a list of numbers that could refer to anything. Let's say that this set here refers to the number of cars sold at a car dealership 4 days in a row.
However, you must put these numbers in numerical order to properly work with them (this isn't necessary to find the mean or the mode, but it is necessary for the range and the median). Our set would now look like this:
{3, 3, 4, 6}
Mean - the mean simply means the average. Add them up (3+3+4+6=16), divide by the number of numbers (4), and you will get a mean or average of 4.
Median - this is the number in the center of the set. When you have an odd number of numbers (such as 1, 2, 3), finding the median is very simple because it is literally the number in the middle (in that case, 2). With our number set above, there is no middle term, which means we simply take the average of the two numbers in the middle. Our two middle numbers are 3 and 4, which have an average of 3.5. Thus, our median is 3.5
Mode - this refers to the number that appears the most in the set. In our case, there are two 3's, which means our mode is 3.
Range - this refers to the difference between the highest and lowest terms in the number set. Our highest is 6, our lowest is 3, and 6-3 = 3. Thus, our range is 3.
Of course, the number of ways that the ACT can ask questions using and about these 4 terms is just about limitless. If you need guided practice in this area, check out my book The ACT Math System.
If you want some free ACT prep cheat sheets that lay it all out in a few pages, then click here!
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