Box Plots

Lesson 8.04

After completing this lesson, you will be able to say:

• I can find the median, quartile, and interquartile range of a set of data.

• I can create a box plot to represent a data set.

• I can make observations about a data set by analyzing a box plot.

Box Plot

Box plot:

Graph showing minimum, maximum, and quartile values for a data set.

There are five pieces of information shown on a box plot:• Minimum: the smallest value in the data set

• Lower Quartile (Q1): the middle value in the lower half of the data set

• Median (Q2): the middle value in the data set

• Upper Quartile (Q3): the middle value of the upper half of the data set

• Maximum: the largest value in the data set

Box Plot

Minimum:Smallest number in a data set

Lower quartile (Q1):Middle value in the lower half of a data set.

Median:Middle number of the data set

Upper Quartile (Q3):Middle value of the upper half of a data set.

Maximum:Biggest number in a data set

Box Plots

Box plots also show what is called interquartile range, or IQR.

Interquartile range (IQR):

The difference between Q3 and Q1; about half the numbers in a data set fall in the interquartile range.

Five-number summary:

To create a box plot, you need the five-number summary for your data set.

Five-number summary:

A summary of the values in a data set; made up of the minimum, lower quartile, median, upper quartile, and maximum.

Five-Number Summary

Minimum: 12Lower quartile: 16Median: 21Upper quartile: 28Maximum: 34

Creating a box plot

To create a box plot:• Draw a number line with a range that includes all the values in your five-

number summary.

• Draw a box above the number line, where the left and right sides are at the lower and upper quartiles.

• Draw a vertical line in the box at the median.

• Draw smaller vertical lines at the minimum and maximum, and connect these lines to the box with horizontal lines.

• Label the line and title the box plot.

Creating a box plot

To start, you need a number line that covers the range of the data set. Then, you draw a box that goes from the lower quartile to the upper quartile. The lower quartile for this data set is 16. The upper quartile is 28.

Creating a box plot

Draw a vertical line at the median to mark the middle of the data set. Because the median value in the five-number summary is 21, draw a short vertical line above 21.

Creating a box plot

Draw horizontal lines extending from the lower and upper quartiles to the minimum and maximum. At the minimum and maximum points, draw a small vertical line to show the minimum and maximum values in the data set.

Creating a box plot

The order in which you plot these items does not make a difference in the final product—just remember to include the title and labels.

Try it!

Here are the ticket prices paid by several groups of fans at a baseball game based on where they are sitting: $25, $19, $44, $32, $53, $33, $26, $38.

What is the five-number summary for this data set? Create a box plot for this data.

Check your work

Reading a Box Plot

You know that box plots can be created from a five-number summary of data. Well, did you know that you can do the opposite and create a five-number summary by reading a box plot?

Let’s use the box plot above to find the five-number summary

Reading a Box Plot - example

First you need the minimum, which is the smallest value. Look at where the left whisker ends. In the plot, this value is twelve.

To find the maximum value, look at the right whisker, which ends at thirty-four.

minimum Maximum

Reading a Box Plot - example

The lower quartile is found at the left side of the box. For the old fitness scores, the lower quartile is fourteen.

The right side of the box ends at thirty, which is the upper quartile.

lower quartile upper quartile

Reading a Box Plot - example

The vertical line inside the box marks the median. The middle number for the old fitness scores is twenty-one.

median

From this, you can also see that the interquartile range is sixteen. The middle fifty percent of values in the data set are between fourteen and thirty.

Reading a Box Plot - example

Try It

Create a five-number summary

Check your work

Now that you completed this lesson, you should be able to say:

• I can find the median, quartile, and interquartile range of a set of data.

• I can create a box plot to represent a data set.

• I can make observations about a data set by analyzing a box plot.