Box Plots

A box plot is a way of visually displaying data which shows different features of the data such as the lowest value, lower quartile, median, upper quartile, highest value, and any outliers that you may have in your data. Box plots can also be used to compare data, this can be done by placing more than one box plot onto the diagram.

Below is an example of a box plot, explaining what each part means.

From a box plot you can then find out the interquartile range. This can be calculated by subtracting the lower quartile from the upper quartile.

For example, in the picture above the interquartile range would be

Using the example above, to find out what would be a lower outlier you can simply calculate it. $5.5-(1.5\times 2)=2.5$ so this means that an outlier will be any piece of data less than 2.5, which is why the data piece marked as 1.5 is classed as an outlier.

How to plot a box plot?

In order to plot a box plot, you need the following,

• Lowest value.

• Lower quartile (Q₁).

• Median (Q₂).

• Upper quartile (Q₃).

• Highest value.

You don't necessarily need an outlier in order to draw a box plot as there may not be any found in the data.

However, sometimes the data may not be presented clearly – you may be given a list of data, as given in the next example.

How to interpret a box plot

It is very important to understand how to interpret a box plot. You should know how to identify the different features that are presented in a box plot as well as using the information you are given to compare box plots. Below is an example of a box plot – let's take a look at it and work through some potential questions you may come across.

The box plot below shows the height of a group of boys,

Interpreting a box plot, Thomas-Gay - StudySmarter Originals

Here are some examples of questions you may be asked about the box plot,

1. What are the lower and upper quartiles?

You know that the upper and lower quartiles are what make up the box, so you can see that the lower quartile is 160.5 and the upper quartile is 165.5.

2. Calculate the interquartile range

To do this you can take the lower quartile and subtract it from the upper quartile,$165.5-160.5=5$

This can be identified by looking at the box plot and finding the middle line of the box, which is 163.

Box plots can also be used to compare data, for example, data representing the height of a group of girls can be placed below the original box plot to help you compare and contrast.

Comparative box plot, Thomas-Gay - Originals

Here are some examples of questions you may be asked about the two box plots.

1. Compare the heights of males and females

For this question, you can describe what you can see on the box plots. The box plots show that males have a higher value and higher median than females, meaning that the males are taller.

2. What is the highest value of heights of females?

For this question you only need to look at the female box plot, it shows that the highest value is 163.

3. A person was measured at a height of 162cm, give a reason why they are more likely to be male or female?

For this question you will need to look at both of the box plots, you can see that there are much more males that had a height of 162 or higher, which means that it is more likely to be a male that was measured at 162.