Stopping Distances

Updated July 2017
Back to Box and Whisker Plots

Topics: Box and Whiskers Plot (Box Plot), five number summary, interquartile range, upper fence, outlier
Mathematical Skills and Concepts:
  • Find, use, and interpret measures of center and spread, including median, interquartile range, and upper fence.
  • Understand box plots usefulness in displaying the degree of dispersion and skewness in the data, and to identify outliers.
  • Discuss and understand the correspondence between data sets and their graphical representations, box plots.

TinkerPlots file

StoppingDistancesPlot.png


Kelly is shopping for a new car. She is very concerned about safety. She found these data about braking distances measured in feet (at 30 mph) for ten different cars of each of the two models (small sedans and large sedans) that she is most seriously considering. The data set is shown below the questions.

Directions:
1. Create parallel box plots with distance on the x-axis and car size on the y-axis. Hide the icons.

2. Practice toggling outliers off and on in the plot.

3. Record the five-point summary for each box plot (scroll over the different segments).

4. Which models seem to have the shortest stopping distance at 30 mph? Explain.

The difference between the first and third quartiles is called the interquartile range (IQR).

5. Calculate the interquartile range (IQR) for each of the model types. You can use the ruler tool. "Snap" each end of the ruler to the sides of the box.
StoppingDistRulerTool.png

6. What does the IQR tell you about the graphed data?

7. Why is the fourth interval for the large sedans missing?

The formula for the upper fence is UF = Q3 + (1.5*IQR).

8. What is the relationship between the upper fence and this data set?

9. What conclusion can you make from the data about the overall stopping distances of these two model types?


This activity was adapted from Navigating through Data Analysis in Grades 6-8, NCTM
Click here to see activity information and solutions

Alternate technology:
GeoGebra

Note that in GeoGebra you will need to use one column of data for small sedans and another column of data for large sedans.

Suggested You Tube Videos on for GeoGebra
Henry Mesa - Statistics Tools: Compare a Histogram to Box Plot

Martin Klausen - Statistics Tools: Parallel box plots not in English

Linda Fahlberg-Stoanovska - Box Plot Command on GeoGebra

Amy Kaye - Box Plot Command on GeoGebra
Roger Marris data set