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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

<< back to Problem H1

 

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!

<< back to Problem H2

 

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.

<< back to Problem H3

 

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

<< back to Problem H4

 

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.

<< back to Problem H5

 

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