# Expert Answers

Last year, a road construction firm hired 11 new employees. Their ages at hiring are listed below. Find the mean hiring age to one decimal place.

23 19 30 33 27 31 58 22 21 26 29

A. 29.1

B. 28.0

C. 29.2

D. 29.0

Al and Joe are two county sheriff’s deputies assigned to watch for traffic violations. Their arrest and conviction records for May and June are shown below.

May June

Arrest Convictions Arrest Convictions

Al 10 2 80 40

joe 90 30 20 12

Who had the best conviction percentage overall?

A. Al

B. Joe

C. They are equal

D. Cannot tell by the data available

The weights (in ounces) of 21 cookies are shown. Find the median weight.

0.62 1.25 0.60 1.62 0.75 0.74 1.35

1.25 1.53 0.99 0.62 1.25 1.28 0.66

0.47 1.25 0.74 1.28 1.72 0.75 0.56

A. 0.99 ounces

B. 1.01 ounces

C. 0.98 ounces

D. 1.00 ounces

Use the range rule of thumb to approximate the standard deviation.

22, 29, 21, 24, 27, 28, 25, 38

A. 3.50

B. 4.0

C. 4.25

D. 2.8

Find the mode(s) for the given sample data. 20, 49, 46, 43, 49, 43, 49, 20, 22

A. 43

B. 49

C. 20

D. 22

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class?

A. The mean will increase; the median will be unchanged.

B. The median will increase; the mean will be unchanged.

C. Neither the mean nor the median will change.

D. Both the median and the mean will increase.

The mathematics SAT scores of the seven students in a mathematics seminar are 538, 550, 570, 593, 610, 622, and 634. Suppose the student with the score 634 drops the seminar and is replaced by a student with a score of 600. What will happen to the mean and the median scores of the class?

A. Neither mean nor median will change.

B. The median will decrease, the mean will not change.

C. The median will not change, the mean will decrease.

D. Both mean and median will decrease.

Use the range rule of thumb to approximate the standard deviation.

496, 598, 503, 528, 565, 601, 576, 543

A. 170.2

B. 60.6

C. 26.25

D. 18.75

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.

22, 29, 21, 24, 27, 28, 25, 36

A. 4.8

B. 4.2

C. 2.8

D. 1.6

The students in Hugh Logan’s math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score.

552 593 358 352 537

349 357 596 470 482

A. 446.8

B. 474.6

C. 462.8

D. 464.6

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the cars it makes. Suppose that the models and mpg’s for a manufacturer are Corsair (31 mpg), Futura (30 mpg), Retro (37 mpg), and Envy (44 mpg). Twenty percent of the cars sold are Corsairs, 30% are Futuras, 40% are Retros, and 10% are Envys. Find the average mpg for this manufacturer.

A. 35.5 mpg

B. 34.0 mpg

C. 34.4 mpg

D. None of the above

Suppose that your income is at the 81st percentile of wage earners in the United States. What percent of wage earners make more than you do?

A. 19%

B. 81%

C. Cannot be calculated from the information given

D. None of the above

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg’s for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 27 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

A. 27 mpg

B. 29 mpg

C. 30 mpg

D. 54 mpg

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 585. What will happen to the mean and the median scores of the class?

A. Neither the mean nor the median will change.

B. Both the median and the mean will increase.

C. The median will increase; the mean will be unchanged.

D. The mean will increase; the median will be unchanged.

The batting averages of the first three batters in the Eureka College women’s softball team lineup are .310, .301, and .277. If the first three batters are considered as the “lead-off group”, what is the batting average of the group?

A. .301

B. .296

C. There is insufficient information to answer the question

D. None of the above

A softball player has a batting average of exactly .300 and no more than

60 times at bat. Suppose this player gets 5 hits in her next 6 times at

bat. What is the highest possible average she could now have?

A. .500

B. .833

C. .348

D. There is insufficient information to answer the question

Find the mode(s) for the given sample data.

66, 25, 66, 13, 25, 29, 56, 66

A. 25

B. 56

C. 25 & 66

D. 66

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be?

A. Symmetric with little variation

B. Symmetric with large variation

C. Skewed right with large variation

D. Skewed left with little variation

23 19 30 33 27 31 58 22 21 26 29

A. 29.1

B. 28.0

C. 29.2

D. 29.0

Al and Joe are two county sheriff’s deputies assigned to watch for traffic violations. Their arrest and conviction records for May and June are shown below.

May June

Arrest Convictions Arrest Convictions

Al 10 2 80 40

joe 90 30 20 12

Who had the best conviction percentage overall?

A. Al

B. Joe

C. They are equal

D. Cannot tell by the data available

The weights (in ounces) of 21 cookies are shown. Find the median weight.

0.62 1.25 0.60 1.62 0.75 0.74 1.35

1.25 1.53 0.99 0.62 1.25 1.28 0.66

0.47 1.25 0.74 1.28 1.72 0.75 0.56

A. 0.99 ounces

B. 1.01 ounces

C. 0.98 ounces

D. 1.00 ounces

Use the range rule of thumb to approximate the standard deviation.

22, 29, 21, 24, 27, 28, 25, 38

A. 3.50

B. 4.0

C. 4.25

D. 2.8

Find the mode(s) for the given sample data. 20, 49, 46, 43, 49, 43, 49, 20, 22

A. 43

B. 49

C. 20

D. 22

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class?

A. The mean will increase; the median will be unchanged.

B. The median will increase; the mean will be unchanged.

C. Neither the mean nor the median will change.

D. Both the median and the mean will increase.

The mathematics SAT scores of the seven students in a mathematics seminar are 538, 550, 570, 593, 610, 622, and 634. Suppose the student with the score 634 drops the seminar and is replaced by a student with a score of 600. What will happen to the mean and the median scores of the class?

A. Neither mean nor median will change.

B. The median will decrease, the mean will not change.

C. The median will not change, the mean will decrease.

D. Both mean and median will decrease.

Use the range rule of thumb to approximate the standard deviation.

496, 598, 503, 528, 565, 601, 576, 543

A. 170.2

B. 60.6

C. 26.25

D. 18.75

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.

22, 29, 21, 24, 27, 28, 25, 36

A. 4.8

B. 4.2

C. 2.8

D. 1.6

The students in Hugh Logan’s math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score.

552 593 358 352 537

349 357 596 470 482

A. 446.8

B. 474.6

C. 462.8

D. 464.6

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the cars it makes. Suppose that the models and mpg’s for a manufacturer are Corsair (31 mpg), Futura (30 mpg), Retro (37 mpg), and Envy (44 mpg). Twenty percent of the cars sold are Corsairs, 30% are Futuras, 40% are Retros, and 10% are Envys. Find the average mpg for this manufacturer.

A. 35.5 mpg

B. 34.0 mpg

C. 34.4 mpg

D. None of the above

Suppose that your income is at the 81st percentile of wage earners in the United States. What percent of wage earners make more than you do?

A. 19%

B. 81%

C. Cannot be calculated from the information given

D. None of the above

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg’s for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 27 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

A. 27 mpg

B. 29 mpg

C. 30 mpg

D. 54 mpg

The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score 533 drops the seminar and is replaced by a student with a score of 585. What will happen to the mean and the median scores of the class?

A. Neither the mean nor the median will change.

B. Both the median and the mean will increase.

C. The median will increase; the mean will be unchanged.

D. The mean will increase; the median will be unchanged.

The batting averages of the first three batters in the Eureka College women’s softball team lineup are .310, .301, and .277. If the first three batters are considered as the “lead-off group”, what is the batting average of the group?

A. .301

B. .296

C. There is insufficient information to answer the question

D. None of the above

A softball player has a batting average of exactly .300 and no more than

60 times at bat. Suppose this player gets 5 hits in her next 6 times at

bat. What is the highest possible average she could now have?

A. .500

B. .833

C. .348

D. There is insufficient information to answer the question

Find the mode(s) for the given sample data.

66, 25, 66, 13, 25, 29, 56, 66

A. 25

B. 56

C. 25 & 66

D. 66

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be?

A. Symmetric with little variation

B. Symmetric with large variation

C. Skewed right with large variation

D. Skewed left with little variation

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