Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 6, Part B:
Comparative Observational Studies

In This Part: A New Raisin Question | Using Five-Number Summaries and Box Plot
The Interquartile Range

Comparing two sets of measurements is not quite as simple as comparing two numbers. Because we are comparing a set of 28 measurements for Brand C with a set of 36 measurements for Brand D, any comparison must be based on percentages and not absolute frequencies. A comparison of the Five-Number Summaries is useful, since these quantities divide the ordered data into four groups, with approximately 25% of the data in each group. Here are the Five-Number Summaries for these data: Note 3

Min

Q1

Med

Q3

Max

 Brand C 25 26 28 29 32 Brand D 23 27 29 33 38

Here are the comparative box plots for these data:

You might start by comparing the actual values in the Five-Number Summaries. This will tell you where one set of measurements is located relative to the other set:

Note that with the exception of the minimum values, all summary measures for Brand D are higher than for Brand C. This suggests that boxes of Brand D tend to have more raisins than boxes of Brand C. In fact, since the third quartile for Brand D is greater than the maximum for Brand C, more than 25% of the boxes of Brand D have more raisins than any boxes of Brand C.

 Session 6: Index | Notes | Solutions | Video