Deck 2: Descriptive Statistics

Question 1

The grade point averages for 40 students are listed below.
Construct an ogive using eight classes.

Answer 1

Question 2

Use the given frequency distribution to construct a cumulative frequency distribution and an ogive.
29

Answer 2

Question 3

Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits,
and the upper class limits.
min =1, max =30,6 classes

Answer 3

Class width = 5, Lower class limits: 1, 6, 11, 16, 21, 26; Upper class limits: 5, 10, 15, 20, 25, 30

Question 4

Use the given frequency distribution to construct a cumulative frequency distribution and an ogive.

Question 5

Use the given frequency distribution to find the
(a)class width.
(b)class midpoints of the first class.
(c)class boundaries of the first class.

- $$\begin{array}{l}\text { Weight (in pounds) }\\\begin{array} { c | c } \text { Class } & \text { Frequency, } \mathrm { f } \\\hline 135 - 139 & 6 \\140 - 144 & 4 \\145 - 149 & 11 \\150 - 154 & 15 \\155 - 159 & 8\end{array}\end{array}$$

A) (a) 5
(b) 137
(c) 134.5-139.5
B) (a) 5
(b) 137
(c) $135 - 139$
C) (a) 4
(b) $137.5$
(c) $134.5 - 139.5$
D) (a) 4
(b) $137.5$
(c) $135 - 139$ 29

Question 6

Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits,
and the upper class limits.

Question 7

Provide an appropriate response.
A sample of candies have weights that vary from 2.35 grams to 4.75 grams. Use this information to find the upper and lower limits of the first class if you wish to construct a frequency distribution with 12 classes.

A)2.35-2.55
B)2.35-2.54
C)2.35-2.65
D)2.35-2.75

Question 8

The grade point averages for 40 students are listed below.
Construct a frequency histogram, a relative frequency histogram and a frequency polygon using eight classes.

Question 9

Provide an appropriate response.
Use the ogive below to approximate the number in the sample.

A)80
B)100
C)341
D)28

Question 10

Use the relative frequency histogram to
a)identify the class with the greatest, and the class with the least, relative frequency.
b)approximate the greatest and least relative frequencies.
c)approximate the relative frequency of the fifth class.

Question 11

Provide an appropriate response.
A city in the Pacific Northwest recorded its highest temperature at 91 degrees Fahrenheit and its lowest temperature at 12 degrees Fahrenheit for a particular year. Use this information to find the upper and lower
Limits of the first class if you wish to construct a frequency distribution with 10 classes.

A)12-19
B)12-20
C)7-17
D)12-18

Question 12

Use the given frequency distribution to construct a cumulative frequency distribution and an ogive.
2
8
5

Question 13

Use the given frequency distribution to construct a frequency histogram, a relative frequency histogram and a frequency
polygon.

Question 14

Use the given frequency distribution to construct a frequency histogram, a relative frequency histogram and a frequency
polygon.

Question 15

Use the given frequency distribution to find the
(a)class width.
(b)class midpoints of the first class.
(c)class boundaries of the first class.

- $$\begin{array}{l}\text { Miles (per day) }\\\begin{array} { c | c } \text { Class } & \text { Frequency, } \mathrm { f } \\\hline 1 - 2 & 9 \\3 - 4 & 22 \\5 - 6 & 28 \\7 - 8 & 15 \\9 - 10 & 4\end{array}\end{array}$$ 2 8
5

A) (a) 2
(b) $1.5$
(c) $0.5 - 2.5$
B) (a) 1
(b) $1.5$
(c) $0.5 - 2.5$
C) (a) 2
(b) 1
(c) $1 - 2$
D) (a) 1
(b) 1
(c) 1-2

Question 16

Use the given frequency distribution to find the
(a)class width.
(b)class midpoints of the first class.
(c)class boundaries of the first class.

- $$\begin{array}{l}\text { Phone Calls (per day) }\\\begin{array} { r | c } { \text { Class } } & \text { Frequency, f } \\\hline 8 - 11 & 18 \\12 - 15 & 23 \\16 - 19 & 38 \\20 - 23 & 47 \\24 - 27 & 32\end{array}\end{array}$$

A) (a) 4
(b) $9.5$
(c) 7.5-11.5
B) (a) 3
(b) $10.5$
(c) $8 = 11$
C) (a) 4
(b) $10.5$
(c) 8-11
D) (a) 3
(b) $9.5$
(c) $7.5 - 11.5$

Question 17

The grade point averages for 40 students are listed below.
Construct a frequency distribution, a relative frequency distribution, and a cumulative frequency distribution
using eight classes. Include the midpoints of the classes.

Question 18

Use the given frequency distribution to find the
(a)class width.
(b)class midpoints of the first class.
(c)class boundaries of the first class.

- $\text { Height (in inches) }$
$\begin{array} { c | c } \text { Class } & \text { Frequency, f } \\\hline 50 - 52 & 5 \\53 - 55 & 8 \\56 - 58 & 12 \\59 - 61 & 13 \\62 - 64 & 11\end{array}$

A) (a) 3
(b) 51
(c) $49.5 - 52.5$
B) (a) 2
(b) $51.5$
(c) $49.5 - 52.5$
C) (a) 3
(b) 51
(c) 50-52
D) (a) 2
(b) $51.5$
(c) $50 - 52$

Question 19

Provide an appropriate response.
Use the ogive below to approximate the cumulative frequency for 24 hours.

A)63
B)17
C)27
D)75

Question 20

Use the given frequency distribution to construct a cumulative frequency distribution and an ogive.

Question 21

Provide an appropriate response.
For the dot plot below, what is the maximum and what is the minimum entry?

A)max: 17; min: 12
B)max: 54; min: 15
C)max: 54; min: 12
D)max: 14; min: 12

Question 22

The Highway Patrol, using radar, checked the speeds (in mph)of 30 passing motorists at a checkpoint. The results are
listed below.
Construct a frequency histogram, a relative frequency histogram and a frequency polygon using six classes.

Question 23

Provide an appropriate response.
A study was conducted to determine how people get jobs. Four hundred subjects were randomly selected and
the results are listed below. Construct a Pareto chart of the data.

Question 24

Provide an appropriate response.
The numbers of home runs that Sammy Sosa hit in the first 15 years of his major league baseball career are
listed below. Make a stem-and-leaf plot for this data. What can you conclude about the data?

Question 25

The heights (in inches)of 30 adult males are listed below.
Construct a frequency polygon using five classes.

Question 26

Provide an appropriate response.

-For the stem-and-leaf plot below, what is the maximum and what is the minimum entry? $$\text { Key : } 11 \mid 9 = 11.9$$ $$\begin{array} { l | l l l l l l l l l l l l } 11 & 6 & 9 & & & & & & & & \\12 & 4 & 6 & 6 & 7 & 8 & 9 & & & & \\13 & 0 & 1 & 1 & 2 & 3 & 6 & 6 & 7 & 8 & 8 \\14 & 3 & 4 & 6 & 6 & 8 & 9 & 9 & 9 & & \\15 & 0 & 1 & 1 & 2 & 3 & 7 & 7 & 8 & 9 & \\16 & 2 & 2 & 5 & 7 & 8 & 8 & 9 & 9 & & \\17 & 7 & 8 & & & & & & & &\end{array}$$

A)max: 17.8; min: 11.6
B)max: 178; min: 116
C)max: 17.7; min: 11.6
D)max: 17.8; min: 11.9

Question 27

Provide an appropriate response.
A study was conducted to determine how people get jobs. Four hundred subjects were randomly selected and
the results are listed below. Construct a pie chart of the data.

Question 28

The Highway Patrol, using radar, checked the speeds (in mph)of 30 passing motorists at a checkpoint. The results are
listed below.
Construct an ogive using six classes.

Question 29

Provide an appropriate response.
The heights (in inches)of 30 adult males are listed below. Construct a dot plot for the data.

Question 30

The heights (in inches)of 30 adult males are listed below.
Construct a relative frequency histogram using five classes.

Question 31

Provide an appropriate response.
The heights (in inches)of 30 adult males are listed below. Construct a stem-and-leaf chart for the data.
What can you conclude about the data?

Question 32

Provide an appropriate response.
Explain the difference between class limits and class boundaries.

Question 33

Provide an appropriate response.
The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are
listed below. Make a stem-and-leaf plot for this data. What can you conclude about the data?

Question 34

The heights (in inches)of 30 adult males are listed below.
Construct a frequency distribution, a relative frequency distribution, and a cumulative frequency distribution
using five classes.

Question 35

The heights (in inches)of 30 adult males are listed below.
Construct a frequency histogram using five classes.

Question 36

Match the description of the sample with the correct plot.

-Time (in minutes)it takes a sample of employees to drive to work

A)
B)
C) Key: $0 \mid 9 = 0.9$
$\begin{array} { l | l } 0 & 9 \\1 & 49 \\2 & 3678 \\3 & 01568 \\4 & 0\end{array}$
D) Key: $7 \mid 2 = 72$
$\begin{array} { l | l l } 6 & 89 \\7 & 0233678 \\8 & 2456778 \\9 & 0115\end{array}$

Question 37

Provide an appropriate response.
Listed below are the ACT scores of 40 randomly selected students at a major university. a)Construct a relative frequency histogram of the data, using eight classes.
b)If the university wants to accept the top 90% of the applicants, what should the minimum score be?
c)If the university sets the minimum score at 17, what percent of the applicants will be accepted?

Question 38

Provide an appropriate response.
The Highway Patrol, using radar, checked the speeds (in mph)of 30 passing motorists at a checkpoint. The
results are listed below. Construct a dot plot for the data.

Question 39

The Highway Patrol, using radar, checked the speeds (in mph)of 30 passing motorists at a checkpoint. The results are
listed below.
Construct a frequency distribution, a relative frequency distribution, and a cumulative frequency distribution
using six classes.

Question 40

Provide an appropriate response.
The Highway Patrol, using radar, checked the speeds (in mph)of 30 passing motorists at a checkpoint. The
results are listed below. Construct a stem-and-leaf plot for the data, listing each stem twice. What can you
conclude about the data?

Question 41

Provide an appropriate response.
The data below represent the smoking prevalence among U.S. adults over a 35-year period. Use a time series
chart to display the data. Describe any trends shown.

Question 42

Provide an appropriate response.
The numbers of home runs that Barry Bonds hit in the first 10 years of his major league baseball career are
listed below. Use a scatter plot to display the data. Is there a relationship between the home runs and the
batting averages?

Question 43

Provide an appropriate response.
Women were allowed to enter the Boston Marathon for the first time in 1972. Listed below are the winning
womenʹs times (in minutes)for the first 10 years. Use a time series chart to display the data.

Question 44

Provide an appropriate response.
The graph below shows the number of car accidents occurring in one city in each of the years 1 through 6. The
number of accidents dropped in year 3 after a new speed limit was imposed. Does the graph distort the data?
How would you redesign the graph to be less misleading?

Question 45

Provide an appropriate response.
A study was conducted to determine how certain families pay on their credit card balances. Two hundred
families with a household annual income between $25,000 and $49,999 were randomly selected and the results
are listed below. Construct a pie chart of the data.

Question 46

Provide an appropriate response.
The number of beds in a sample of 24 hospitals are listed below. Construct a stem -and-leaf plot for the data.

Question 47

Provide an appropriate response.
The lengths, in kilometers, of the worldʹs largest subway systems are listed below. Construct a Pareto chart for
the data.

Question 48

Provide an appropriate response.
The data below represent the alcohol-related driving fatalities, in thousands, in the United States over a
20-year period. Use a time series chart to display the data. Describe any trends shown.

Question 49

Provide an appropriate response.
The heights (in inches)of 30 adult males are listed below. Construct a Pareto chart for the data.

Question 50

Provide an appropriate response.
The data below represent the numbers of absences and the final grades of 15 randomly selected students from a
statistics class. Use a scatter plot to display the data. Is there a relationship between the studentsʹ absences and
their final grades?

Question 51

For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe
the shape of the histogram as symmetric, uniform, skewed left, or skewed right.

-Data set: California Pick Three Lottery $$\begin{array} { l l l l l l l l l l } 3 & 6 & 7 & 6 & 0 & 6 & 1 & 7 & 8 & 4 \\1 & 5 & 7 & 5 & 9 & 1 & 5 & 3 & 9 & 9 \\2 & 2 & 3 & 0 & 8 & 8 & 4 & 0 & 2 & 4\end{array}$$

A)uniform
B)symmetric
C)skewed left
D)skewed right

Question 52

Provide an appropriate response.
A safety engineer wishes to use the following data to show the number of deaths from the collision of
passenger cars with trucks on a particular highway. Use a time series chart to display the data. Describe any
trends shown.

Question 53

Provide an appropriate response.
The five longest winning streaks for NCAA Menʹs Division I Basketball are listed below. Construct a Pareto
chart for the data.

Question 54

Provide an appropriate response.

-Find the mean, median, and mode of the data.

A) $\bar { x } = 70 ; \text { median } = 69 ; \text { mode } = 67$
B) $\bar { x } \approx 70.1 ; \text { median } = 69 ; \text { mode } = 68$
C) $\bar { x } \approx 70.3 ; \text { median } = 69 ; \text { mode } = 68$
D) $\bar { x } = 70 ; \text { median } = 67 ; \text { mode } = 69$

Question 55

Provide an appropriate response.
Of the 55 tornado fatalities in a recent year, the locations of the victims are listed below. Construct a pie chart
of the data.

Question 56

Provide an appropriate response.
Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

A)skewed left
B)skewed right
C)symmetric
D)uniform

Question 57

Provide an appropriate response.
Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

A)skewed right
B)skewed left
C)symmetric
D)uniform

Question 58

Provide an appropriate response.
The data below represent the infant mortality rates and the life expectancies for seven selected countries in
Africa. Use a scatter plot to display the data.

Question 59

Provide an appropriate response.
The number of minutes that a dentist kept 20 patients waiting beyond their appointment times are listed below.
Construct a stem-and-leaf plot for the data.

Question 60

Provide an appropriate response.
Use a scatter plot to display the data below. All measurements are in milligrams per cigarette.

Question 61

Provide an appropriate response.

-The scores of the top ten finishers in a recent golf tournament are listed below. Find the mode score. $$\begin{array} { l l l l l l l l l l } 71 & 67 & 67 & 72 & 76 & 72 & 73 & 68 & 72 & 72\end{array}$$

A)72
B)67
C)76
D)73

Question 62

Provide an appropriate response.
The amounts of money won by the top ten finishers in a recent Daytona 500 are listed below. Find the mean
and median winnings. Round to the nearest dollar. Which measure- the mean or the median- best represents
the data? Explain your reasoning.

Question 63

Provide an appropriate response.
Use the histogram below to approximate the mode heart rate of adults in the gym.

A)70
B)42
C)55
D)2

Question 64

Provide an appropriate response.

-The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the mean speed. $$\begin{array} { l l l l l l l } 181.1 & 202.2 & 190.1 & 201.4 & 191.3 & 201.4 & 192.2 \\201.2 & 193.2 & 201.2 & 194.5 & 199.2 & 196.0 & 196.2\end{array}$$

A)195.8
B)196.1
C)201.2
D)210.9

Question 65

Provide an appropriate response.

-The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the mode speed. $$\begin{array} { l l l l l l l } 181.1 & 202.2 & 190.1 & 201.4 & 191.3 & 201.4 & 192.2 \\201.2 & 193.2 & 201.2 & 194.5 & 199.2 & 196.0 & 196.2\end{array}$$

A)bimodal: 201.2, 201.4
B)201.4
C)201.2
D)no mode

Question 66

Provide an appropriate response.
A student receives test scores of 62, 83, and 91. The studentʹs final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is
15% of the final grade. What is the studentʹs mean score in the class?

A)80.6
B)76.6
C)90.6
D)85.6

Question 67

Provide an appropriate response.

-The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed. $$\begin{array} { l l l l l l l } 181.1 & 202.2 & 190.1 & 201.4 & 191.3 & 201.4 & 192.2 \\201.2 & 193.2 & 201.2 & 194.5 & 199.2 & 196.0 & 196.2\end{array}$$

A)196.1
B)196.7
C)195.8
D)201.2

Question 68

Provide an appropriate response.

-The scores of the top ten finishers in a recent golf tournament are listed below. Find the median score. $$\begin{array} { l l l l l l l l l l } 67 & 67 & 68 & 71 & 72 & 72 & 72 & 72 & 73 & 76\end{array}$$

A)72
B)67
C)71
D)73

Question 69

Provide an appropriate response.
The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are
listed below. Find the mean and median number of home runs. Round the mean to the nearest whole number.
Which measure of central tendency- the mean or the median- best represents the data? Explain your
reasoning.

Question 70

Provide an appropriate response.
Find the mean, median, and mode of the following numbers:

Question 71

Provide an appropriate response.
Use the histogram below to approximate the median heart rate of adults in the gym.

A)70
B)65
C)75
D)42

Question 72

Approximate the mean of the frequency distribution.

- $$\begin{array} { c | c } \text { Miles (per day) } & \text { Frequency } \\\hline 1 - 2 & 15 \\3 - 4 & 28 \\5 - 6 & 11 \\7 - 8 & 14 \\9 - 10 & 9\end{array}$$

A)5
B)4
C)6
D)15

Question 73

For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe
the shape of the histogram as symmetric, uniform, skewed left, or skewed right.

-Data set: ages of 20 cars randomly selected in a student parking lot $$\begin{array} { r r r r r r r r r r } 12 & 6 & 4 & 9 & 11 & 1 & 7 & 8 & 9 & 8 \\9 & 13 & 5 & 15 & 7 & 6 & 8 & 8 & 2 & 1\end{array}$$

A)symmetric
B)uniform
C)skewed left
D)skewed right

Question 74

Approximate the mean of the frequency distribution.

- $$\begin{array} { c | c } \text { Phone calls (per day) } & \text { Frequency } \\\hline 8 - 11 & 37 \\12 - 15 & 49 \\16 - 19 & 17 \\20 - 23 & 46 \\24 - 27 & 39\end{array}$$

A)18
B)17
C)16
D)19
E)38

Question 75

Provide an appropriate response.

-The scores of the top ten finishers in a recent golf tournament are listed below. Find the mean score. $$\begin{array} { l l l l l l l l l l } 71 & 67 & 67 & 72 & 76 & 72 & 73 & 68 & 72 & 72\end{array}$$

A)71
B)67
C)68
D)72

Question 76

For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe
the shape of the histogram as symmetric, uniform, skewed left, or skewed right.

-Data set: systolic blood pressures of 20 randomly selected patients at a blood bank $$\begin{array} { l l l l l l l l c l } 135 & 120 & 115 & 132 & 136 & 124 & 119 & 145 & 98 & 110 \\125 & 120 & 115 & 130 & 140 & 105 & 116 & 121 & 125 & 108\end{array}$$

A)symmetric
B)uniform
C)skewed left
D)skewed right

Question 77

Provide an appropriate response.
Use the histogram below to approximate the mean heart rate of adults in the gym.

A)70.8
B)1425.7
C)70
D)31.6

Question 78

Provide an appropriate response.
Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives an A in a four-credit class, a D in a two-credit class, a B in a three-credit
Class and a C in a three-credit class, what is the studentʹs grade point average?

A)2.75
B)1.75
C)2.50
D)3.00

Question 79

Provide an appropriate response.
The numbers of runs batted in that Sammy Sosa hit in the first 15 years of his major league baseball career are
listed below. Find the mean and median number of runs batted in. Round the mean to the nearest whole
number.

Question 80

For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe
the shape of the histogram as symmetric, uniform, skewed left, or skewed right.

-Data set: California Pick Three Lottery $$\begin{array} { l l l l l l l l l l } 8 & 6 & 7 & 6 & 0 & 9 & 1 & 7 & 8 & 4 \\1 & 5 & 7 & 5 & 9 & 7 & 5 & 3 & 9 & 9 \\8 & 8 & 3 & 9 & 8 & 8 & 9 & 0 & 2 & 7\end{array}$$

A)skewed left
B)symmetric
C)uniform
D)skewed right