# Box & Whiskers

## Introduction

Box and whiskers allow us to graphically represent the spread of data by showing the quartiles. This type of diagram is called Box and whiskers because it consists of boxes that have lines extending from them called whiskers. They are quite easy to create and give us a lot of information about the set of data.

### Creating Box and Whiskers Plots

We need a set of numerical values (data) to create a box and whiskers diagram. Let’s use the following number sequence: 2,4,5,6,8,9,11 Next we have to find the min and max value as well as the quartiles and the median. Let’s start off with the median. The median is the middle number and in this case 6. The min and max values are 2 and 11. To find the quartiles we have to cut the number sequence into quarters. 2,4,5,6,8,9,11 You can put in lines to separate the numbers. The numbers under the lines are the quartiles: 4, 6 & 9. We have already found 6 as the median or middle quartile. 4 is the lower quartile and 9 is the upper quartile. Now we can plot the box and whiskers. This is what a typical box and whiskers looks like. Look at the graph to see how we plotted it. We used all the values that we found before to create the box and whiskers. The line separating the boxes is the median:6. The lines where the boxes end are the other two quartiles: 4 and 9. Then we simply have to draw á horizontal line on both sides with a line at the end. These lines represent the min and max values. The thickness of the bar usually doesn’t matter.

### Working with Box and Whiskers

When looking at box and whiskers we can find: Median Lower Quartile Upper Quartile Lowest Value Largest Value Interquartile Range Interquartile Range The interquartile range is the range between the two quartiles. It is calculate by subtracting the upper quartile from the lower quartile: 9 - 4 = 6 In this example, the interquartile range is 6.

## More Data Lessons

If you haven’t looked at the other methods for presenting data yet, you should do so. You can also have a look at probability or processing data. If you would like to study a completely different topic, have a look in our library. Please share this page if you like it or found it helpful!
ULTIMATE MATHS
WHERE MATHS IS AT YOUR FINGERTIPS!
MIN: 2 (Lowest Value)
MAX: 11 (Largest Value)
Median: 6 (Middle Value)
LQ: 4 (Lower Quartile)
UQ: 9 (Upper Quartile)
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Chapter 22.7:  Learning Outcomes Students will learn how to create box and whiskers! Students will learn how to work with Box & Whisker plots!