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Calculating & Interpreting Quartiles

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  • 0:01 What is a Quartile?
  • 1:05 How to Find a Quartile
  • 3:15 Example
  • 4:30 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

If you're going to divide a data set into four groups in order to make a box and whisker plot, then it would likely be very helpful to know where to split the data. Quartiles tell you exactly where to make the divisions.

What Is a Quartile?

Imagine that you had a gigantic set of data to analyze. Okay, maybe not gigantic, but still big enough to want to split it up into four parts. Why four parts? Well, if you've used a box and whisker chart, you can see that it's incredibly useful for showing range and spread of data. But even if you haven't, four is still a pretty good number. After all, people can internalize what it is to be in the best or worst quarter, but ask them how they feel about being in the fifth-seventh and you might get some strange looks.

Of course, to be able to divide a set of data into four pieces, you have to know where to make the cuts. Just like a surgeon should, hopefully, know where to cut open a leg to help set a badly broken bone, so too must you know where to cut your data. Luckily, you don't have to deal with blood.

The name given to where to cut your data into four equal groups is known as a quartile. In this lesson, we'll learn how to find them, as well as go through an example of using quartiles in action.

How to Find a Quartile

So, how do you go about finding a quartile? Simply ask yourself how you would find the middle point of a collection of numbers. If you're not new to working with numbers as data, then you probably know that the middle point of a collection of numbers is the median. If you remember how to calculate the median, then you're already ahead of the game. If not, simply put the numbers in order and determine what the middle point is. If it's between two numbers, just take the average. In any event, that's the median.

It also happens to be one of the quartiles. We call this quartile Q2, since it is the second quartile. Keep in mind that there only three quartiles, since these three slices divide the data into four chunks. These groups are equal in that they all contain the same number of data points, but can span different ranges. At Q2, 50% of the data is on either side of the quartile while at Q1, 25% of the data is less than the quartile. Likewise at Q3, 25% of the data is greater than the quartile.

So that's one quartile, but what about the other two? Simple - do the same thing again, but this time replace the far end point with the median. As a result, if you are trying to find Q1, the first quartile that cuts between the lowest two quarters of a set, then you find the median between the median of the whole set and the lowest number.

Likewise, if you're trying to find Q3, the third quartile that cuts between the highest two quarters of the set, then find the median between the median for the whole set and the highest number. Remember to divide the two numbers on either side if the median falls in between numbers.

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