Box-and-Whisker Plot/Boxplot

In this tutorial, you're going to learn about a graphical display called a boxplot. This will cover:

1. Boxplots
2. Two or more distributions

1. Boxplots

Boxplots are also sometimes called box and whisker plots.

Boxplot/Box-and-Whisker Plot

A graphical distribution of the five number summary. The "box" in the middle contains the middle 50% of the values, and the "whiskers" extend out to the maximum and minimum values from the quartiles.

A boxplot is a way to graphically display the five number summary for a data set.

Suppose you have a chart of the heights of the Chicago Bulls basketball team.

The five number summary consists of:

• The minimum value, which is the shortest individual on the team: 71 inches
• The maximum, which is the highest value in the data set (the tallest individual on the team): 84
• The three quartiles:
  1. the first quartile, which is the value at which 25% percent of the data falls at or below: 74
  2. the median, which is the value at which 50% of the data falls at or below: 79
  3. the third quartile, which is the value at which 75% of the data falls at or below: 81

So how do you put this information into a boxplot?

1. First draw an axis. It can be horizontal or vertical.

2. Second, scale it with equal increments. Here, the graph goes from the lowest number, 71, and a little bit lower, to the tallest number, 84.

3. Then, make a mark where the five numbers from the five number summary are: 71, 74, 79, 81, and 84.

4. Next, draw a box from the first quartile to the third quartile.

The box shows where 50% of the data lies, the middle 50%. About 25% percent of the data falls in the "whisker" to the left side, and about 25% of the data falls in a "whisker" to the right hand side.

This is why it's sometimes called a box and whisker plot.

2. Two or more distributions

You can use boxplots to compare two distributions. For instance, if we were talking about the heights of girls vs boys, we might be able to compare them by saying the spread, or the variation, with the girls, is much less than the variation with boys.

You'll notice the boxplots in this statistical package don't have vertical lines at the edges:

You can see that variability not only in the width of the boxes, but also in the total from the minimum to the maximum in each of these two data sets. So boxplots can be a sort of a summary distribution for the boys and for the girls.

Boxplots allow you to display, visually, the five number summary. You can interpret a boxplot to see if the data points are close together, where the vertical lines are close together, and where the data points are further apart. With boxplots, you can analyze skewness or look for symmetry. And you can use multiple boxplots on the same set of axes that will help you compare two or more distributions.

Thank you and good luck!