Session 2 Solutions

B C D E
Homework

Solutions for Session 2, Homework

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

Problem H1

Brand A

Brand B

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

Brand D

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

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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!

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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.

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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

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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.

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Session 2 | Notes | Solutions | Video