## Introduction

Boxplots get their name from what they resemble. They are sometimes referred to as box and whisker plots. These types of graphs are used to display the range, median, and quartiles. When they are completed, a box contains the first and third quartiles. Whiskers extend from the box to the minimum and maximum values of the data.

The following pages will show how to make a boxplot for a set of data with minimum 20, first quartile 25, median 32, third quartile 35 and maximum 43.

## Number Line

Begin with a number line that will fit your data. Be sure to label your number line with the appropriate numbers so that others looking at it will know what scale you are using.

## Median, Quartiles, Maximum and Minimum

Draw five vertical lines above the number line, one for each of the values of the minimum, first quartile, median, third quartile and maximum. Typically the lines for the minimum and maximum are shorter than the lines for the quartiles and median.

For our data, the minimum is 20, the first quartile is 25, the median is 32, the third quartile is 35 and the maximum is 43. The lines corresponding to these values are drawn above.

## Draw a Box

Next, we draw a box and use some of the lines to guide us. The first quartile is the left-hand side of our box. The third quartile is the right-hand side of our box. The median falls anywhere inside of the box.

By the definition of the first and third quartiles, half of all of the data values are contained within the box.

## Draw Two Whiskers

Now we see how a box and whisker graph gets the second part of its name. Whiskers are drawn to demonstrate the range of the data. Draw a horizontal line from the line for the minimum to the left side of the box at the first quartile. This is one of our whiskers. Draw a second horizontal line from the rights side of the box at the third quartile to the line representing the maximum of the data. This is our second whisker.

Our box and whisker graph, or boxplot, is now complete. At a glance, we can determine the range of the values of the data, and the degree to how bunched up everything is. The next step shows how we can compare and contrast two boxplots.

## Comparing Data

Box and whisker graphs display the five-number summary of a set of data. Two different data sets can thus be compared by examining their boxplots together. Above a second boxplot has been drawn above the one that we have constructed.

There are a couple of features that deserve mention. The first is that the medians of both sets of data are identical. The vertical line inside both of the boxes is at the same place on the number line. The second thing to note about the two box and whisker graphs is that the top plot is not as spread out at the bottom one. The top box is smaller and the whiskers do not extend as far.

Drawing two boxplots above the same number line supposes that the data behind each deserve to be compared. It would make no sense to compare a boxplot of heights of third graders with weights of dogs at a local shelter. Although both contain data at the ratio level of measurement, there is no reason to compare the data.

On the other hand, it would make sense to compare boxplots of third graders' heights if one plot represented the data from the boys in a school, and the other plot represented the data from the girls in the school.