7.3. Box-and-Whisker Plots http://www.ck12.org
7.3 Box-and-Whisker Plots
Learning Objectives
- Construct a box-and-whisker plot.
- Construct and interpret a box-and-whisker plot.
- Construct box-and-whisker plots for comparison.
- Use technology to create box-and-whisker plots.
Introduction
An oil company claims that its premium grade gasoline contains an additive that significantly increases gas mileage.
To prove their claim the selected 15 drivers and first filled each of their cars with 45L of regular gasoline and asked
them to record their mileage. Then they filled each of the cars with 45L of premium gasoline and again asked them
to record their mileage. The results below show the number of kilometers each car traveled.
Display each set of data to explain whether or not the claim made by the oil company is true or false.
We will revisit this problem later in the lesson to determine whether or not the oil company did place an additive in
its premium gasoline that improved gas mileage.
Box-and-Whisker Plot
A box-and-whisker plot is another type of graph used to display data. It shows how the data are dispersed around
a median, but does not show specific values in the data. It does not show a distribution in as much detail as does a
stem-and-leaf plot or a histogram, but it clearly shows where the data is located. This type of graph is often used
when the number of data values is large or when two or more data sets are being compared. The center of the
distribution, its spread and the range of the data are very obvious form the graph. The box-and-whisker plot (often
called a box plot), divides the data into quarters by use of the medians of these quarters.
As we construct a box-and-whisker plot for a given set of data, you will understand how this type of graph is very
useful in statistics.
Example 1:
You have a summer job working at Paddy’s Pond which is a recreational fishing spot where children can go to catch
salmon which have been raised in a nearby fish hatchery and then transferred into the pond. The cost of fishing
depends upon the length of the fish caught ($0.75 per inch). Your job is to transfer 15 fish into the pond three times
a day. Before the fish are transferred, you must measure the length of each one and record the results. Below are the
lengths (in inches) of the first 15 fish you transferred to the pond: