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Instructor’s Resource Guide Understandable Statistics, 8th Edition

CHAPTER 3 TEST FORM A 1. A random sample of 18 airline carry-on luggage bags gave the following weights (rounded to the nearest pound). 12 41

25 7

10 22

38 10

12 19

19 12

8 16

12 5

17 14

Find the mean, median, and mode of these weights.

1. _____________________________

2. Find the mean and the 5% trimmed mean for the following annual salaries (in thousands) of employees in a small company. Which is most representative of the average annual salary? Why? 38.5 34.2

31.0 38.6

29.8 187.4

37.4 40.6

40.1 39.7

35.1 31.0

41.5 29.8

2. _____________________________ 12.6 42.0

39.7 30.8

28.4 35.5

3. A random sample of 7 Northern Pike from Taltson Lake (Canada) gave the following lengths rounded to the nearest inch. 21

27

46

35

41

36

25

(a) Find the range.

3. (a) __________________________

(b) Find the sample mean.

(b) __________________________

(c) Find the sample variance.

(c) __________________________

(d) Find the sample standard deviation.

(d) __________________________

4. A random sample of receipts for individuals eating at the Terrace Restaurant showed the sample mean to be x = $10.38 with sample standard deviation s = $2.17. (a) Compute the coefficient of variation for this data. (b) Use Chevyshev’s Theorem to find the smallest interval centered on the mean in which we can expect at least 75% of the data to fall.

4. (a) __________________________

(b) __________________________

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Part III: Sample Tests, Chapter 3

81

CHAPTER 3, FORM A, PAGE 2 5. A random sample of 330 adults were asked the maximal amount (dollars) they would spend on a ticket to a top rated performance. The results follow where x is the cost and f is the number of people who would spend that maximal amount. x

20

30

40

50

60

f

62

83

120

40

25

(a) Compute the sample mean.

5. (a) __________________________

(b) Compute the sample variance.

(b) __________________________

(c) Compute the sample standard deviation.

(c) __________________________

6. A random sample of 27 skiers at Vail, Colorado gave their ages. The results were 18 62 49

25 47 52

32 56 37

16 19 26

41 22 72

52 38 44

29 15 19

58 46 24

23 33 29

(a) Give the five number summary including the low value Q1, median, Q3 and high value.

6. (a) __________________________

(b) Make a box-and-whisker plot for the given data.

(b)

(c) Find the interquartile range.

(c) __________________________

7. In Biology 340, weights are assigned to required activities as follows: project, 25%; exam 1, 15%; exam 2, 15%; exam 3, 15%; final exam, 30% Each activity is graded on a 100 point scale. Gary earned 75 points on the project, 85 points on exam 1, 95 points on exam 2, 90 points on exam 3, and 88 points on the final exam. Compute his overall weighted average in the Biology 340 class. 7. _____________________________ 8. Lifestyles Weight-loss Clinic gave the following information about the distribution of its clients. Estimate the weighted average of the weight (in pounds) of a client. Weight (lb) Clients

8. _____________________________

130−149

150−169

170−189

190−209

11%

48%

32%

7%

9. Sophia took a test and scored in the 79th percentile. What percentage of the scores were at or below her score? What percentage were above?

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9. _____________________________

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Instructor’s Resource Guide Understandable Statistics, 8th Edition

CHAPTER 3 TEST FORM B 1. A veterinarian in a small animal clinic had the following record of life spans of Golden Retrievers (to the nearest year). 9 13

12 6

15 11

11 16

8 11

10 14

7 11

5 4

11 12

14 11

Find the mean, median, and mode for this data.

1. _____________________________

2. Find the mean and the 10% trimmed mean for the following annual snowfalls (in inches) for a city in northern Wisconsin. Which is most representative of the average annual snowfall? Why? 24

37

28

13

38

29

112

21

40

2. _____________________________ 36

3. A random sample of 6 people, each 20 pounds overweight, volunteered to go on the same diet. After 3 months, their weight loss (in pounds) were 12

5

14

19

15

8

(a) Find the range.

3. (a) __________________________

(b) Find the sample mean.

(b) __________________________

(c) Find the sample variance.

(c) __________________________

(d) Find the sample standard deviation.

(d) __________________________

4. A large sample of Northern Pike caught at Taltson Lake (Canada) showed that the average length was x = 32.5 inches with sample standard deviation s = 8.6 inches. (a) Compute the coefficient of variation for this data. (b) Use Chevyshev’s Theorem to find an interval centered on the mean in which we can expect at least 75% of the data to fall.

4. (a) __________________________

(b) __________________________

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Part III: Sample Tests, Chapter 3

83

CHAPTER 3, FORM B, PAGE 2 5. A random sample of 146 students in Chemistry 215 gave the following grade information (A = 4.0, B = 3.0, C = 2.0, D = 1.0, and F = 0). In the following table x = grade and f = number of students receiving this grade. x

0

1

2

3

4

f

8

14

62

43

19

(a) Find the sample mean. (b) Find the sample variance. (c) Find the sample standard deviation.

5. (a) __________________________ (b) __________________________ (c) __________________________

6. A random sample of 24 professors at Montana State University gave the following ages (years). 29 36 44

32 47 39

56 41 28

61 68 46

27 59 42

43 40 62

38 33 58

65 35 45

(a) Give the five number summary including the low value Q1, median, Q3 and high value.

6. (a) __________________________

(b) Make a box-and-whisker plot for the given data.

(b)

(c) Find the interquartile range.

(c) __________________________

7. A teacher rating system uses the following items and weights: Availability, 10%; Clarity of presentation, 25% Respectful of student ideas, 20%; Grades fairly, 15%; Knowledge of the field, 30% Each item is rated on a 100 point scale. Dr. Gill was evaluated by her Sociology 350 class and received the following ratings: Availability, 65; Clarity, 85; Respects students, 90; Grades fairly, 70; Knowledge, 95. Compute a weighted average to determine Dr. Gills overall teacher rating. 7. _____________________________ 8. Famous Framing gave the following information about the distribution of costs and sales. Estimate the weighted average of the cost (in dollars) of a sale. 8. _____________________________ Cost ($) Sales

10−26 2%

27−43 15%

44−60 48%

61−77 23%

9. Tyler took a test and scored in the 81st percentile. What percent of scores were above his score? What percent were at or below his score?

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78−94 12%

9. _____________________________

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Instructor’s Resource Guide Understandable Statistics, 8th Edition

CHAPTER 3 TEST FORM C Write the letter of the response that best answers each problem. 1. The durations of a random sample of 16 commercials are below (in seconds). Find the mean, median, and mode of these durations. 30 55

12 8

26 35

7 18

14 42

35 15

20 30

1. __________

30 10

(a) Mean = 24.19, median = 30, mode = 23 (b) Mean = 20.13, median = 21, mode = 35 (c) Mean = 24.19, median = 23, mode = 30 (d) Mean = 20, median = 24.19, mode = 30 (e) Mean = 30, median = 20, mode = 22.13

2. Find the 5% trimmed mean for the following heights of fruit trees (in feet) in Gordy’s Farm Market. 5.2 4.1 8.2 1.3

6.5 3.7 4.9 6.0

7.4 7.4 7.3 5.8

8.0 6.9 6.1 4.3

(a) 6.05 ft

(b) 6.27 ft

(c) 5.80 ft

(d) 6.16 ft

9.1 5.5 7.2 5.4

7.6 4.0 6.5 6.5

5.4 3.9 3.4 7.6

3.1 5.2 8.6 9.0

4.7 5.8 4.7 6.7

2. __________

15.0 7.2 5.8 13.4

(e) 6.36 ft

3. A random sample of 9 Walleye Pike from Salty Lake gave the following weights rounded to the nearest pound. 3

4

11

6

5

7

6

2

4

A. Find the range. (a) 4

(b) 5

3. A. __________ (c) 7

(d) 8

(e) 9

B. Find the sample mean. (a) 5.33

(b) 9

B. __________ (c) 7

(d) 2.65

(e) 5

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Part III: Sample Tests, Chapter 3

85

CHAPTER 3, FORM C, PAGE 2 C. Find the sample variance. (a) 2.65

(b) 5

C. __________

(c) 7

(d) 5.33

(e) 6.22

D. Find the sample standard deviation. (a) 5.33

(b) 7

(c) 2.49

D. __________ (d) 2.65

(e) 6.22

4. A random sample of 30 receipts for individuals shopping at the Community Drug Store showed the sample mean to be x = $28.19 with sample standard deviation s = $4.06. A. Compute the coefficient of variation for this data. (a) 6.94%

(b) 14.4%

(c) 694%

4. A. __________

(d) 4.32%

(e) 0.48%

B. Use Chevyshev’s Theorem to find the smallest interval centered on the mean in which we can expect at least 88.9% of the data to fall. (a) 16.01 to 40.37

(b) 24.13 to 28.19

(c) 20.07 to 36.31

(d) 11.95 to 44.43

B. __________

(e) 24.13 to 32.25

5. A random sample of 210 high school students were asked how many hours per week they spent studying at home. The results follow where x is the hours and f is the number of students who spend that amount of time. x

3

5

7

9

11

f

30

45

70

55

10

A. Compute the sample mean. (a) 0.025

(b) 40.29

5. A. __________ (c) 6.71

(d) 0.149

(e) 6

B. Compute the sample variance. (a) 4.871

(b) 2.212

B. __________ (c) 199

(d) 210

(e) 4.894

C. Compute the sample variance. (a) 4.894

(b) 4.871

C. __________ (c) 2.207

(d) 2.212

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(e) 14.11

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Instructor’s Resource Guide Understandable Statistics, 8th Edition

CHAPTER 3, FORM C, PAGE 3 6. What are the numbers used in making a box-and-whisker plot?

6. __________

(a) Low value, Q1, mean, Q3, high value (b) Low value, Q1, median, Q3, high value (c) s, mean, s2, interquartile range (d) Q1, Q2, Q3 (e) Low value, interquartile range, high value

7. In Chemistry 400, weights are assigned to required activities as follows: class participation, 15%; exam 1, 20%; exam 2, 20%; exam 3, 20%; laboratory 25% Each activity is graded on a 100 point scale. Mary earned 70 points on class participation, 80 points on exam 1, 64 points on exam 2, 77 points on exam 3, and 96 points on laboratory. Compute her overall weighted average in the Chemistry 400 class. (a) 78.7

(b) 77.4

(c) 100

(d) 78.2

(e) Cannot determine

8. Calico Corner gave the following information about the distribution of cost and sales. Estimate the weighted average of the cost (in dollars) of a sale. Cost ($) Sales

20−29 64%

(a) 80.44

(b) 29.2

(c) 29.7

(d) 30.2

30−39 23%

40−49 10%

(b) 13%

8. __________

50−59 3%

(e) Cannot determine

9. Luke took a test and scored in the 88th percentile. What percentage of the scores were above his score? (a) 87%

7. __________

(c) 89%

(d) 88%

9. __________

(e) 12%

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