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Learning Math Home
Data Session 6, Part B: Comparative Observational Studies
 
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Session 6, Part B:
Comparative Observational Studies

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

Your comparison of the two sets of measurements should also consider the degree of variation within each set. This comparison can be based on the range of all the data (Max - Min) as well as on the range of the middle half of the data (which is called the Q-Spread or Interquartile Range, or simply the IQR), which is found by subtracting Q1 from Q3.

Let's look at the box plots again, and then calculate the range and the IQR:

 

Range (Max - Min)

IQR (Q3 - Q1)

Brand C

32 - 25 = 7

29 - 26 = 3

Brand D

38 - 23 = 15

33 - 27 = 6

Based on the comparative box plots, there is more variation in the raisin counts for Brand D raisins than for Brand C raisins. The values for the ranges and IQR confirm this (Range C = 7, Range D = 15; IQR C = 3, IQR D = 6). Both the range and the IQR for Brand D are at least twice the range and the IQR for Brand C.

Consequently, although Brand D tends to have more raisins per box than Brand C, the smaller range and IQR for Brand C tell us that Brand C is more consistent than Brand D. Since the weights of boxes are the same, this would also suggest that the sizes of the raisins vary less for Brand C.

Problem B2

Solution  

Brand A raisins come in boxes of the same weight as Brands C and D. Here are the ordered counts for 30 boxes of Brand A raisins:

Brand A

23 25 25 26 26 26 26 27 27 27 27
28 29 29 29 30 30 31 31 31 32 32
32 33 34 34 35 35 36 39

Compare the counts for Brands A and D. Make sure you consider where the data are located and the degree of variation. (You may have already determined the Five-Number Summary in Session 4.)


 

Problem B3

Solution  

Brand B raisins come in boxes of the same weight as Brands A, C, and D. Here are the ordered counts for 27 boxes of Brand B raisins:

Brand B

17 22 24 24 25 25 25 25 26 26 26 26 26 26 27 27 27 27 28 29 29 29 29 29 29 30 30

Compare the counts for three brands: A, B, and C. Make sure you consider where the data are located and the degree of variation. (You may have already determined the Five-Number Summary in Session 4.)


Next > Part C: Comparative Experimental Studies

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