Deck 4: Describing Data

Question 1

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

Answer 1

49

Question 2

Use the range rule of thumb to approximate the standard deviation. 15, 42, 63, 7, 9, 12, 14, 28, 47

A) 8.0
B) 29.1
C) 15.8
D) 14.0

Answer 2

D

Question 3

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. $\begin{array} { l l l l } 23 & 19 & 30 & 33 \end{array}$
$\begin{array} { l l l l } 27 & 31 & 58 & 22 \end{array}$
$\begin{array} { l l l } 21 & 26 & 29 \end{array}$

Answer 3

29.0

Question 4

The number of vehicles passing through a pharmacy drive-up line with two windows during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period. $$\begin{array} { r r r r } 16 & 8 & 17 & 24 \\24 & 22 & 26 & 23 \\30 & 19 & 7 & 25 \\18 & 27 & 21 & 16 \\11 & 15 & 20 & 14\end{array}$$

Question 5

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. $$\begin{array} {c} \quad { \text { May } } \quad \quad \quad \quad \quad\quad \quad \quad{ \text { June } } \\\begin{array} { | l | l | l | l | l | } \hline & \text { Arrests } & \text { Convictions } & \text { Arrests } & \text { Convictions } \\\hline \text { Al } & 10 & 2 & 80 & 40 \\\hline \text { Joe } & 90 & 30 & 20 & 12 \\\hline\end{array}\end{array}$$ Who had the best conviction percentage in May?
Who had the best conviction percentage in June?
Who had the best conviction percentage overall?

Question 6

The salaries of ten randomly selected doctors are shown below.
$$\begin{array} { l l l l l } \$ 105,000 & \$ 149,000 & \$ 163,000 & \$ 214,000 & \$ 225,000 \\\$ 116,000 & \$ 111,000 & \$ 791,000 & \$ 240,000 & \$ 178,000\end{array}$$
Find the median salary.

Question 7

The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data set.
$\begin{array}{llllllllll}5.5 & 5.7 & 5.8 & 5.9 & 6.1 & 6.1 & 6.3 & 6.4 & 6.5 & 6.6 \\ 6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \\ 7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7\end{array}$

A)


B)


C)


D)

Question 8

Suppose that there are 400 students in your school class. What class rank is the 20th percentile?

A) 80
B) 40
C) 20
D) None of the above

Question 9

The distances traveled (in miles) to 8 different swim meets are given below:
73, 24, 46, 34, 61, 10, 86, 52
Find the median distance traveled.

Question 10

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

Question 11

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

Question 12

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

Question 13

Consider the distribution of weights of all the Juniors at Bloomington High School. How many peaks would you expect in the graph of the distribution?

A) 3
B) 0
C) 2
D) 1

Question 14

Find the mode(s) for the given sample data.
7.29, 7.41, 7.56, 7.29, 7.88, 7.99, 7.62

A) 7.56
B) 7.29
C) 7.577
D) 7.41

Question 15

Which of the distributions has the greatest variation?

A)


B)


C)

Question 16

Which of the distributions is symmetric?

A)


B)


C)


D)

Question 17

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
2, 6, 15, 9, 11, 22, 1, 4, 8, 19

A) 2.1
B) 6.3
C) 6.8
D) 7.1

Question 18

The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score.
$$\begin{array} { l l l l l } 552 & 593 & 358 & 352 & 537 \\349 & 357 & 596 & 470 & 482\end{array}$$

Question 19

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.

Question 20

The blood types for 30 people who agreed to participate in a medical study were as follows. Find the mode(s) of the blood types.

Question 21

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

Question 22

Which of the distributions has the greatest variation?

A)


B)


C)

Question 23

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.

Question 24

The following data set is the GPAs of the students in a statistics class.
What percentile is a GPA of 2.34?

A) About the 6th
B) About the 15th
C) About the 30th
D) About the 60th

Question 25

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.

Question 26

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

Question 27

The grocery expenses for six families were $80.86, $47.74, $57.92, $81.08, $75.18, and $88.08. Compute the mean grocery bill. Round your answer to the nearest cent.

Question 28

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 four of the five models of a manufacturer are 19, 22, 28, and 26, and the manufacturer just meets the government standard of 31 mpg. Find the mileage for the fifth model.

A) 60 mpg
B) 31 mpg
C) 24 mpg
D) 19 mpg

Question 29

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
15, 42, 53, 7, 9, 12, 14, 28, 47

A) 29.1
B) 16.6
C) 17.8
D) 15.8

Question 30

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. Who had the best conviction percentage in May?
Who had the best conviction percentage in June?
Who had the best conviction percentage overall?

Question 31

The table shows the country represented by the winner of the 10,000 meter run in the Summer Olympic Games in various years.
$$\begin{array} { l l | l l } \text { Year } & \text { Country } & \text { Year } & \text { Country } \\\hline 1912 & \text { Finland } & 1968 & \text { Kenya } \\1920 & \text { Finland } & 1972 & \text { Finland } \\1924 & \text { Finland } & 1976 & \text { Finland } \\1928 & \text { Finland } & 1980 & \text { Ethiopia } \\1932 & \text { Poland } & 1984 & \text { Italy } \\1936 & \text { Finland } & 1988 & \text { Morocco } \\1948 & \text { Czechoslovakia } & 1992 & \text { Morocco } \\1952 & \text { Czechoslovakia } & 1996 & \text { Ethiopia } \\1956 & \text { USSR } & 2000 & \text { Ethiopia } \\1960 & \text { USSR } & 2004 & \text { Ethiopia } \\1964 & \text { United States } & 2008 & \text { Ethiopia } \\& & 2012 & \text { Britain }\end{array}$$ Find the mode of the country data.

Question 32

The test scores of 32 students are listed below. Construct a boxplot for the data set.
$\begin{array}{llllllll}32 & 37 & 41 & 44 & 46 & 48 & 53 & 55 \\ 57 & 57 & 59 & 63 & 65 & 66 & 68 & 69 \\ 70 & 71 & 74 & 74 & 75 & 77 & 78 & 79 \\ 81 & 82 & 83 & 86 & 89 & 92 & 95 & 99\end{array}$

A)


B)


C)


D)

Question 33

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the average mpg for the four models manufactured is 24 mpg and the government standard is 31 mpg. The manufacturer will add a model. What mileage must the new model get so that the manufacturer meets the government
Requirement?

A) 32 mpg
B) 38 mpg
C)59 mpg
D) None of the above

Question 34

Which of the distributions is skewed to the right?

A)


B)


C)

Question 35

Consider the distribution of heights of all the players in the national Basketball Association. What would you expect the shape of the distribution to be?

A) Skewed right
B) Skewed left
C) Symmetric

Question 36

The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the median of the data.
$\begin{array} { l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 \end{array}$
$\begin{array} { l l l l l } 3.9 & 1.0 & 3.6 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.7 & 2.2 & 1.5 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 2.7 & 0.4 & 3.7 & 2.0 & 3.6 \end{array}$

Question 37

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.

Question 38

Find the mode(s) for the given sample data.
66, 25, 66, 13, 25, 29, 56, 66

Question 39

The host of a dinner party purchases wine based on the weighted average of clarity (10%), bouquet (5%), friendliness to the palate (5%), storage ability of opened bottles (40%), and price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and 9, respectively. What is its rating?

A) 5.80
B) 5.00
C) 7.60
D) None of the previous

Question 40

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.
88, 84, 209, 151, 271, 242, 234
Find the median number of newspapers sold.

Question 41

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

Question 42

Six football players, all defensive linemen, decide that they will gain an average of 10 pounds over the summer. At the start of the season, only five showed up for the weigh-in. They had gained 9, 13, 11, 6, and 7 pounds. How many pounds does the last person have to gain in order that the group can attain its goal?

Question 43

In a basketball player's first three seasons in the NBA, his field goal percentage is .340, .450, and .480. In those three seasons, the number of field goals he attempted was 80, 400, and 520 respectively. What is his career field goal percentage after three years?

Question 44

Which of the distributions is skewed to the right?

A)


B)


C)

Question 45

Which one of the distributions shown below is left skewed?

A)


B)


C)

Question 46

Which one of distributions shown below has the least variation?

A)



B)


C)

Question 47

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

Question 48

Alex is 80th in his class of 320 students. What is his percentile rank in class?

Question 49

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

Question 50

The test scores of 40 students are listed below. Construct a boxplot for the data set.
$\begin{array}{llllllllll}25 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \\ 59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \\ 72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \\ 81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98\end{array}$

A)


B)



C)


D)

Question 51

The number of people waiting in the cash register lines at a local supermarket were 4, 3, 5, 4, 3, 2, 3
Find the mode(s) of these data.

Question 52

Which of the distributions is multimodal?

A)


B)


C)

Question 53

In testing a new light bulb design, 6 bulbs were left on until they burned out or 2000 hours whichever came first. One bulb had not burned out by the end of the test, so 2000 hours was Recorded for that bulb. If the testers had waited for that bulb to burn out, what would have Happened to the mean and median lives of the bulbs?

A) Neither mean nor median would have changed.
B) Both mean and median would increase.
C) The mean would increase, but the median would not change.
D) The median would increase, but the mean would not change.

Question 54

Amtrak trains from Chicago to Portland arrived at Havre, MT, where they make a crew change, the following numbers of minutes late.
26, 17, 245, 19, 38, 42, 11, 0, 14, 44
Find the mean number of minutes late at Havre (to one decimal place).

Question 55

Randomly selected voters leaving the polls identified themselves as Republican (R), Democrat (D), or Independent (I). The data were
R R I D D D I R D D I R R D D
D D I I R I R I D D R I R D I
What is the mode of these data?

Question 56

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.

$$\begin{array} {c} \quad \quad \quad { \text { May } } \quad \quad\quad \quad \quad{ \text { June } } \\\begin{array} { | l | l | l | l | l | } \hline & \text { Arrests } & \text { Convictions } & \text { Arrests } & \text { Convictions } \\\hline\text { Al } & 10 & 1 & 80 & 41 \\\hline \text { Joe } & 90 & 30 & 20 & 12 \\\hline\end{array}\end{array}$$ Who had the best conviction percentage in May?
Who had the best conviction percentage in June?
Who had the best conviction percentage overall?

Question 57

The salaries of randomly selected bank employees were
$$\begin{array} { l l l l l } \$ 23,540 & \$ 82,500 & \$ 37,360 & \$ 24,670 & \$ 19,810 \\\$ 33,140 & \$ 22,940 & \$ 27,420 & \$ 47,130 & \$ 29,290\end{array}$$
Find the median salary of these employees.

Question 58

Randomly selected high school seniors had the following numbers of one-dollar bills in their wallets.
2, 4, 3, 7, 5, 4, 5, 2, 9, 17, 0, 4, 7, 6, 8
Find the median number of one-dollar bills.

Question 59

A trout hatchery had more 4 year-old fish than they could use one year, so they held about 1000 of them over until the next year. The hatchery routinely moved fish from one pond to the next each year and 10,000 three-year old fish were placed in the pond with the leftover four-year old fish. When the fish were finally taken out of the pond for releasing into streams, what would the distribution of the weights of the released fish look like? Describe the
distribution as well as you can and draw a picture.

Question 60

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

Question 61

The lengths of 25 "4-inch" bolts, measured with a micrometer are (in inches)
$$\begin{array} { l l l l l } 3.882 & 4.150 & 4.001 & 4.058 & 4.109 \\3.882 & 4.040 & 4.000 & 3.929 & 4.199 \\4.083 & 4.074 & 4.012 & 3.740 & 3.912 \\3.975 & 3.993 & 4.007 & 3.951 & 3.989 \\3.973 & 3.999 & 3.992 & 3.999 & 4.094\end{array}$$ Construct a box plot for these data.

Question 62

Use the range rule of thumb to approximate the standard deviation for the data in Problem 14 to 2 decimal places.

Question 63

The heights of 10 randomly selected fourth grade boys are (in inches) are $$\begin{array} { l l l l l l l l l l } 53 & 53 & 54 & 56 & 56 & 56 & 50 & 57 & 59 & 56\end{array}$$
Find the sample standard deviation s to 2 decimal places.

Question 64

A graduate school accepted candidates as shown in the table below. $$\begin{array} { | l | l | l | } \hline & \text { White } & \text { Non-white } \\\hline \text { Male } & 11 \text { out of } 32 & 12 \text { out of } 31 \\\hline \text { Female } & 58 \text { out of } 80 & 14 \text { out of } 18 \\\hline\end{array}$$
Explain why this table is an illustration of Simpson's paradox. Compare admission rates for White vs Non-white.