B C D EHomework

Solutions for Session 2, Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5

Problem H1

Brand A

Raisin Count

Frequency

Cumulative Frequency

 23 1 1 24 0 1 25 2 3 26 4 7 27 4 11 28 1 12 29 3 15 30 2 17 31 3 20 32 3 23 33 1 24 34 2 26 35 2 28 36 1 29 37 0 29 38 0 29 39 1 30

Brand B

Raisin Count

Frequency

Cumulative Frequency

 17 1 1 18 0 1 19 0 1 20 0 1 21 0 1 22 1 2 23 0 2 24 2 4 25 4 8 26 6 14 27 4 18 28 1 19 29 6 25 30 2 27

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

Raisin Count

Frequency

Cumulative Frequency

 25 3 3 26 5 8 27 3 11 28 9 20 29 3 23 30 2 25 31 1 26 32 2 28

Brand D

Raisin Count

Frequency

Cumulative Frequency

 23 1 1 24 1 2 25 3 5 26 0 5 27 8 13 28 2 15 29 6 21 30 1 22 31 1 23 32 2 25 33 3 28 34 2 30 35 3 33 36 2 35 37 0 35 38 1 36

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:

 Raisin Count Frequency Relative Frequency Fraction Decimal %
 23 1 1/30 .033 3.3 24 0 0/30 .000 0.0 25 2 2/30 .067 6.7 26 4 4/30 .133 13.3 27 4 4/30 .133 13.3 28 1 1/30 .033 3.3 29 3 3/30 .100 10.0 30 2 2/30 .067 6.7 31 3 3/30 .100 10.0 32 3 3/30 .100 10.0 33 1 1/30 .033 3.3 34 2 2/30 .067 6.7 35 2 2/30 .067 6.7 36 1 1/30 .033 3.3 37 0 0/30 .000 0.0 38 0 0/30 .000 0.0 39 1 1/30 .033 3.3

 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.