Once we have the Five-Number Summary, we can display it using a kind of graph known as a box plot. Here is the box plot for the noodle data we've been using:
The box plot is also called a box-and-whiskers plot. Though it looks very different from previous graphs, it's just another way to represent the distribution of the data we've been working with all along:
The lower whisker extends from Min to Q1. The length of this whisker indicates the range of the lowest (or, in this case, the shortest) fourth of the ordered data.
The upper whisker extends from Q3 to Max. The length of this whisker indicates the range of the highest (or, in this case, the longest) fourth of the ordered data.
The box (the rectangular portion of the graph) extends from Q1 to Q3, with a horizontal line segment indicating Med.
The portion of the rectangle between Q1 and Med indicates the range of the second fourth of the ordered data.
The portion of the rectangle between Med and Q3 indicates the range of the third fourth of the ordered data.
The entire rectangle indicates the range of the middle half (the interquartile range) of the ordered data.
Note that the box plots can be drawn vertically or horizontally, depending on whether you display the Five-Number Summary along a vertical or a horizontal axis. Note 2
Video Segment In this video segment, Professor Kader introduces the process of building a box plot. Watch this segment to review the process or to help you draw the box plots for the following problem.
Note: The data set used by the onscreen participants is different from the one provided above.
If you're using a VCR, you can find this segment on the session video approximately 15 minutes and 10 seconds after the Annenberg Media logo.
Let's compare our noodle data as represented by the Five-Noodle Summary, the Five-Number Summary, and the box plot:
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this illustration which doesn't require the Flash plug-in, review the sequence of illustrations on the previous page and on this page, to follow the progression from noodles through box plot.
Using the same scale for each plot, create a box plot for each of the data sets below, which we first saw in Session 2. Each is an ordered list of the number of raisins in a group of boxes from a particular brand. You may want to save your data for use in Session 6.
Start by listing the position for each value in the data set. For example, in the set of Brand A raisins, the value 23 is in the first position, 25 is in the second position, the second 25 is in the third position, and so forth. Close Tip
Compare the two box plots from Problem D2 side by side. What conclusions can you draw about Brand A raisins in comparison to Brand B raisins, using only the box plots?
Video Segment In this video segment, Professor Kader and participants use the box plot to compare different brands of raisins. They then discuss the usefulness of the box plot as a summary of data. Watch this segment after completing Problem D3.
Note: The data sets used by the onscreen participants is different from the ones provided above.
Is the box plot more useful for making comparisons between different distributions than a line plot? Why or why not?
If you're using a VCR, you can find this segment on the session video approximately 18 minutes and 18 seconds after the Annenberg Media logo.
FATHOM Dynamic StatisticsTM Software used with permission of Key Curriculum Press.