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# Data Organization and Representation Session 2: Homework

Problem H1

For the following data sets, create line plots, frequency tables, and cumulative frequency tables. Use your results to answer the question “How many raisins are in a half-ounce box of raisins?” for each brand.

Problem H2

Based on your analyses in Problem H1, which brand of raisins would you buy? Explain.

Problem H3

a. Use the representations of the data you developed for Problem H1 to determine the minimum and maximum raisin counts and the median raisin count for each brand of raisins (A, B, C, and D).

b. Which brand has the most variation? Which has the least variation?

c. Which brand typically has more raisins? Which brand typically has fewer raisins?

d. Does your work on this problem change your answer to Problem H2?

Problem H4

Choose one of the brands listed above and create a relative frequency table and relative frequency bar graph for it.

Problem H5

Create two data sets that have the same mean, the same median, and the same mode, but are not identical data sets. How could you distinguish these sets from each other?

Friel, Susan, Bright, George, and Curcio, Frances (November-December, 1997). Understanding Students’ Understanding of Graphs. Mathematics Teaching in the Middle School, 3 (3), 224-227.
Reproduced with permission from Mathematics Teaching in the Middle School. Copyright © 1997 by the National Council of Teachers of Mathematics. All rights reserved.

Understanding Students’ Understanding of Graphs
Continued

Kader, Gary, and Perry, Mike (November-December, 1997). Pennies from Heaven — Nickels from Where? Mathematics Teaching in the Middle School, 3(3), 240-248.
Reproduced with permission from Mathematics Teaching in the Middle School. Copyright © 1997 by the National Council of Teachers of Mathematics. All rights reserved.

Pennies from Heaven — Nickels from Where?
Continued
Continued
Continued

Putt, Ian; Jones, Graham; Thornton, Carol; Langrall, Cynthia; Mooney, Edward; and Perry, Bob (Autumn, 1999). Young Students’ Informal Statistical Knowledge. Teaching Statistics, 21 (3), 74-78.
This article first appeared in Teaching Statistics <http://science.ntu.ac.uk/rsscse/ts/> and is used with permission.

Young Students’ Informal Statistical Knowledge

### Solutions

Problem H1

Brand A: There are between 23 and 39 raisins in a box. It is 67% likely (20 of 30) that a box will have between 26 and 32 raisins.

Brand B: There are between 17 and 30 raisins in a box. It is 78% likely (21 of 27) that a box will have between 25 and 29 raisins.

Brand C: There are between 25 and 32 raisins in a box. It is 82% likely (23 of 28) that a box will have between 25 and 29 raisins.

Brand D: There are between 23 and 38 raisins in a box. It is 83% likely (30 of 36) that a box will have between 27 and 36 raisins

Problem H2
Answers will vary. Many will choose Brand A, since it has the greatest likelihood (50%) of having at least 30 raisins and has the largest median (29.5). Some will choose Brand C, since it is very unlikely to have 25 raisins or less in a box. Of course, those who don’t like raisins will choose Brand B!

Problem H3
a.  Brand A: minimum = 23, median = 29.5, maximum = 39
Brand B: minimum = 17, median = 26, maximum = 30
Brand C: minimum = 25, median = 28, maximum = 32
Brand D: minimum = 23, median = 29, maximum = 38

b.  Brands A and D each have a larger range than B and C. Although Brand A has the wider range (39 – 23 = 16), Brand D has more extreme values than Brand A.

c. Brand A typically has the most raisins; it has the highest maximum and highest median. Brand B has the fewest raisins.

d.  Answers will vary.

Problem H4
Here are the calculations for Brand A:

Problem H5
There are many possible answers. Here’s one:

Set A: {10, 10, 20, 20, 20, 30, 30}
Set B: {19, 19, 20, 20, 20, 21, 21}

In each set, the mean, median, and mode are all 20. They are not identical; one distinguishing characteristic is the variation in the data. Set A has more variation, with four elements that are each 10 away from the mean. In Set B, all elements are within one of the mean.