. A variable is a characteristic that changes or varies over time, and/or for different individuals or objects under consideration. An experimental unit is the individual or object on which a variable is measured.
a.
True
b.
False
ANSWER:
POINTS:
1
QUESTION TYPE:
True / False
HAS VARIABLES:
DATE CREATED:
2/4/2019 3:06 AM
DATE MODIFIED:
2. Bar and pie charts are graphical techniques for qualitative data. The former focus the attention on the frequency of the occurrences of the categories, and the later emphasize the percentage of occurrences of each category.
3. In a sample of 1000 students in a university, 125 of them or 12.5% are biology majors. The 12.5% is an example of statistical inference.
4. Individual observations within each class may be found in a frequency distribution.
5. Twenty-five percent of a sample of 200 professional tennis players indicated that their parents did not play tennis. This is an example of descriptive statistics as opposed to inferential statistics.
6. A local cable system using a sample of 1000 subscribers estimates that fifty percent of its subscribers watch premium channel at least five times per week. This is an example of inferential statistics as opposed to descriptive statistics.
7. Statistical inference is the process of making an estimate, prediction, or decision about a population based on sample data.
8. In the term "frequency distribution," frequency refers to the number of data values or measurements falling within each class.
9. A branch of the statistics discipline that is used to develop and utilize techniques for effectively presenting numerical information is called inferential statistics.
10. A branch of the statistics discipline that is used to develop and utilize techniques for properly making inferences about population characteristics from information contained in a sample drawn from this population is called inferential statistics.
11. Persons or objects that have characteristics of interest to statisticians are called variables.
12. A qualitative variable about which observations can be made in only two categories is a bivariate data set.
13. A variable that is normally described in words rather than numerically is a qualitative variable.
14. A discrete quantitative variable is one that can assume values only at specific points on an interval of values, with inevitable gaps between them.
15. A continuous quantitative variable is one that can assume values at all points on an interval of values, with no gaps between possible values.
16. Persons or objects on which an experiment is performed are called experimental units.
17. Groupings of data, created to enhance an understanding of them, usually by making the groups collectively exhaustive and mutually exclusive are called classes or categories.
18. A tabular summary of categorical data set showing the number of observations that fall into each of several collectively exhaustive and mutually exclusive classes is called a bar chart.
19. A relative frequency distribution is a tabular summary of a data set showing the proportions of all observations that fall into each of several collectively exhaustive and mutually exclusive classes.
20. Descriptive statistics deals with methods of:
organizing data
summarizing data
c.
presenting data in a convenient and informative way
d.
all of the above
e.
only organizing and summarizing data
d
Multiple Choice
3/15/2019 4:47 AM
21. The relative frequency of a class is computed by:
dividing the frequency of the class by the number of classes
dividing the frequency of the class by the class width
dividing the frequency of the class by the total number of observations in the data set
subtracting the lower limit of the class from the upper limit and multiplying the difference by the number of classes
adding the lower limit of the class to the upper limit and multiplying the sum by the number of classes
c
22. Which of the following is not the goal of descriptive statistics?
displaying aspects of the collected data
reporting numerical findings
estimating characteristics of the population based on a sample
none of these
23. You asked ten of your classmates about their weight. Based on this information, you stated that the average weight of all students in your university or college is 158 pounds. This is an example of:
descriptive statistics
statistical inference
sample
population
sample and population
b
3/15/2019 4:50 AM
24. The best type of chart for comparing two sets of qualitative data is:
a line chart
a pie chart
a histogram
a bar chart
all of these
25. The sum of the frequencies for all classes will always equal:
the number of classes
the class width
the total number of observations in the data set
one
the average
26. The two graphical techniques we usually use to present qualitative data are:
bar chart and histogram
histogram and pie chart
bar chart and pie chart
line chart and stem and leaf plot
bar chart and line chart
27. Which of the following statements is true?
Univariate data result when a single variable is measured on a single experimental unit.
Bivariate data result when less than two variables are measured on a single experimental unit.
Multivariate data result when more than two variables are measured.
Both univariate data result when a single variable is measured on a single experimental unit and multivariate data result when more than two variables are measured are true.
Both bivariate data result when less than two variables are measured on a single experimental unit and multivariate data result when more than two variables are measured are true.
28. Characteristics possessed by experimental units are called:
data sets
internal data
variables
29. A politician who is running for the office of governor of a state with 7 million registered voters commissions a survey. In the survey, 55% of the 10,000 registered voters interviewed say they plan to vote for her. The population of interest is the:
7 million registered voters in the state
10,000 registered voters interviewed
55 %, or 5,500 voters interviewed who plan to vote for her
45%, or 4,500 voters interviewed who plan not to vote for her
55% of the 7 million registered voters in the state
a
30. Which of the following statements is correct?
Bivariate data result when two variables are measured on a single experimental unit.
All of these statements are true.
None of these statements is true.
31. The set of all possible observations about a specified characteristic of interest is:
a frame
a multinomial data set
an observational study
a population
32. A single observation about s specified characteristic of interest is:
a datum
an elementary unit
a univariate data set
3/15/2019 5:01 AM
33. A listing of data in order of ascending or descending magnitude is called:
a frequency distribution
a relative frequency distribution
a relative frequency histogram
34. Which of the following statements is false?
When constructing a frequency distribution for categorical data, it will always be necessary to develop class boundaries.
It is often a good idea to convert frequency distributions to relative frequency distributions when you compare two distributions with different amount of data.
A pie is the familiar circular graph that shows how the measurements are distributed among the categories of a qualitative variable.
None of these.
All of these.
35. A market share of 78.5 percent would be represented in a pie chart by a slice with a central angle of:
78.5 degrees
39.3 degrees
282.6 degrees
141.3 degrees
157 degrees
36. Which of the following statements is true?
In constructing a pie chart for a categorical variable, one sector of the pie is assigned to each category of the variable.
A bar chart for a categorical variable shows the same distribution of measurements in categories as the pie chart, but with the height of each bar measuring how often a particular category was observed.
The categories for a qualitative variable should be chosen so that a measurement will belong to one and only one category, and each measurement has a category to which it can be assigned.
In constructing a pie chart for a categorical variable, one sector of the pie is assigned to each category of the variable and a bar chart for a categorical variable shows the same distribution of measurements in categories as the pie chart, but with the height of each bar measuring how often a particular category was observed.
e
37. A hospital administration would like to know the average length that a patient stays in the hospital. It would be almost impossible to look through all of the past records and average the lengths of stay. Instead, a sample of 1000 patients over the last year was randomly chosen and their lengths of stay were averaged. Describe the population and sample in this problem.Population: ________________________________________________________Sample: ________________________________________________________
The lengths of stay of all the patients that the hospital has ever had; The lengths of stay of the 1000 patients sampled
Subjective Short Answer
STUDENT ENTRY MODE:
Basic
38. A highway department would like to repair a certain highway during the slowest part of a day to help minimize traffic congestion. Because it would be impossible to monitor the traffic flow on every day, they monitor how many vehicles pass on this highway during one particular day. Based on these results the department decides when to repair the highway. Describe the population and sample in this problem.
Population: ________________________________________________________
Sample: ________________________________________________________
All the traffic flow on all days on that highway; The vehicles that passed on that highway on the particular day they recorded
3/15/2019 5:04 AM
39. The freshness and overall quality of milk depend upon the type of packaging used. The manager of a dairy company is considering changing the packaging from cartons to plastic. The quality control team of this dairy company packaged milk in 100 containers of each type of material. After a specific amount of time, the team tested the milk for freshness and overall quality. Identify the population and sample in this problem.Population: ________________________________________________________Sample: ________________________________________________________
All of the milk packaged at this particular dairy company; The 100 selected containers of each type of packaging
40. Identify each of the following variables as either quantitative or qualitative.a. The brands of ice cream that you purchase.______________b. The daily high temperature for the last four weeks.______________c. The amount of sugar consumed by Americans in one year.______________d. The species of fish in the zoo.______________e. The lengths of time children wait for the school bus.______________f. Your favorite professional football team.______________
qualitative; quantitative; quantitative; qualitative; quantitative; qualitative
41. Identify each of the following variables as either quantitative or qualitative.a. Rating of the effectiveness of a new cold remedy (Not effective, effective).______________b. Amount of time spent assembling a five-shelf bookcase.______________c. Number of children in a beginning swimming class.______________d. University where a student is enrolled.______________e. Color preference for a nursery.______________f. Rating the U.S. foreign policy in the Middle East (fair, biased).______________
qualitative; quantitative; quantitative; qualitative; qualitative; qualitative
42. Identify each of the following quantitative variables as discrete or continuous.a. Average monthly temperature for a particular city.______________b. Number of employees of a statistical consulting firm that own laptop computers.______________c. Flight time between two cities.______________d. Number of puppies enrolled in an obedience class.______________e. Number of persons on a flight from Chicago to Los Angeles.______________f. Amount of gas purchased at a gas station.______________
continuous; discrete; continuous; discrete; discrete; continuous
43. Classify the following variables as qualitative or quantitative. If quantitative, further classify as discrete or continuous.a. The colors of cars at an auction.______________b. The amount of money spent building a new school.______________c. The genders of U.S. Senators.______________d. The styles of houses (one-story, two-story, split level, etc.).______________e. The letter grades of students in a statistics exam (A, B, C, D, F).______________f. The number of credit cards owned by customers.______________
qualitative; quantitative,discrete; qualitative; qualitative; qualitative; quantitative, discrete
44. Classify the following variables as qualitative or quantitative. If quantitative, further classify as discrete or continuous.
a. The breeds of cats living in Washington.
______________
b. The weights of male students.
c. The blood group of patients.
d. The treatment received by subjects in the experiment (A, B, or C).
e. The education level of school principals.
f. The number of mobile phones owned per household.
qualitative; quantitative, continuous; qualitative; qualitative; qualitative; quantitative, discrete
3/15/2019 5:46 AM
45. Describe the difference between a population and a sample, and provide two examples for each.
A population is the collection of all measurements of interest to the investigator in a particular study. A sample is a subset of measurements selected from the population of interest; Population: all website visitors; Sample: website visitors who participated in the survey; Population: men aged 40-55 years; Sample: men who participated in the study
Essay
3/15/2019 5:59 AM
46. Describe the difference between descriptive statistics and inferential statistics, and give an example for each.
Descriptive statistics consists of procedures used to summarize and describe the important characteristics of a set of measurements. Inferential statistics consists of procedures used to make inferences about population characteristics from information contained in a sample drawn from this population; Descriptive statistics: The researcher determines average salaries for various occupations in Ohio; Inferential statistics: The researcher wants to test a new flu vaccine. She divides participants of the experiment into two groups. The first group receives new vaccine. The second group receives placebo. The researcher measures the number of people who get flu in both groups. Then she analyzes the measurements and concludes whether the new vaccine is effective or not for all people.
3/15/2019 6:54 AM
47. A bar chart in which the bars are ordered from smallest to largest is called a Pareto chart.
2/4/2019 3:07 AM
48. A relative frequency distribution describes the proportion of data values that fall within each class, and may be presented in a histogram form.
49. Compared to the relative frequency histogram, the stem and leaf plot provides more details, since it can describe the individual data values as well as show how many are in each group, or stem.
3/15/2019 6:17 AM
50. The difference between a histogram and a bar chart is that the histogram represents quantitative data while the bar chart represents qualitative data.
51. The largest value in a set of data is 100, and the lowest value is 20. If the resulting frequency distribution is to have five classes of equal width, the class width will be 16.
52. A relative frequency distribution describes the proportion of data values that fall within each class.
3/19/2019 3:42 AM
53. The class interval in a frequency distribution is the number of data values falling within each class.
54. A stem and leaf plot describes two-digit integers between 30 and 80. For one of the classes displayed, the row appears as 5|234. The numerical values being described are 25, 35, and 45.
3/15/2019 7:45 AM
55. The total area of the six bars in a relative frequency histogram for which the width of each bar is five units is 5.
56. When a distribution has a greater proportion of the measurements to the right of the peak value, we say that it is skewed to the left.
3/15/2019 7:51 AM
57. Time series data are often graphically depicted on a line chart, which is a plot of the variable of interest over time.
58. When a distribution has a greater proportion of the measurements to the left of the peak value, we say that it is skewed to the right.
3/15/2019 7:53 AM
59. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.
60. A skewed histogram is one with a long tail extending either to the right or to the left.
3/15/2019 7:54 AM
61. A dotplot is a graphical portrayal of an absolute or relative frequency distribution of continuous quantitative data in such a way that lower and upper limits of data classes are identified by tick marks on a horizontal axis, while the corresponding absolute or relative class frequencies are represented by the areas of contiguous rectangles that stand on top of each of these class intervals.
62. A pie chart is a portrayal of divisions of some aggregate by a segmented circle in such a way that the sector areas are proportional to the sizes of the divisions in question.
3/15/2019 7:56 AM
63. For the same data, a relative frequency histogram will have the same overall shape as a frequency histogram.
3/15/2019 7:58 AM
64. When constructing a relative frequency distribution, if the data are discrete, it will always be necessary to develop class boundaries.
65. Relative frequency distributions are specifically constructed for analyzing discrete data.
66. If you wish to compare two data sets of different sizes, it is usually a good idea to convert frequency distributions to relative frequency distributions.
67. A relative frequency histogram can be constructed for qualitative as well as quantitative data.
68. A relative frequency histogram can be constructed by letting the horizontal axis or the vertical axis represent the variable of interest.
69. The four classes: less than 5, 5 to < 10, 10 to < 20, greater than 20, would be acceptable for developing a frequency distribution.
3/19/2019 3:36 AM
70. Stem and leaf plots are often used to analyze qualitative data in most real life applications.
71. One of the differences between a bar chart and a histogram is that a histogram typically displays data in a percentage form.
72. Bar charts can typically be formed with the bars vertical or horizontal without affecting the interpretation.
73. In a line chart, the horizontal axis represents time (such as months, years) and the vertical axis represents the value of the variable of interest.
74. The data values plotted on a line graph are connected with a straight line between each pair of successive points.
75. The common graphical presentation of qualitative data is the:
stem and leaf plot
histogram
pie chart
dotplot
time series plot
3/15/2019 8:10 AM
76. Which of the following statements is not true?
One form of descriptive statistics uses graphical techniques.
One form of descriptive statistics uses numerical techniques.
A distribution is skewed to the left if it contains a few unusually large measurements.
Statistical inference is used to draw conclusions or inferences about characteristics of populations based on sample data.
A distribution is not symmetric if it is skewed to the left.
3/15/2019 8:15 AM
77. The total area of the six bars in a relative frequency histogram for which the width of each bar is ten units is:
6
10
16
60
78. The total area of the bars in a relative frequency histogram:
depends on the sample size
depends on the number of bars
depends on the width of each bar
depends on the population size
depends on the frequency
79. In general, incomes of employees in large firms tend to be:
skewed to the right
skewed to the left
symmetric
unknown
80. The sum of relative frequencies found in a relative frequency distribution for quantitative data necessarily equals:
0
100
n, the number of observations in the data set
the number of collectively exhaustive and mutually exclusive classes in a frequency distribution
3/18/2019 1:41 PM
81. Which of the following best describes a relative class frequency?
It is the number of observations that fall into a given class in a frequency distribution.
It is the proportion of all observations that fall into a given class in a frequency distribution.
It is the difference between the numerical lower and upper limit of a class of quantitative data.
It is the number of observations that fall into the smallest class in a frequency distribution.
3/18/2019 1:42 PM
82. Given 180 observations, a data class with an absolute class frequency of 36 must have a relative class frequency of:
.10
.20
.36
.18
83. A graphical portrayal of a relative frequency distribution of continuous quantitative data in such a way that lower and upper limits of data classes are identified by tick marks on a horizontal axis, while the corresponding relative class frequencies are represented by the areas of vertical rectangles connected to each other and stand on top of each of these class intervals, is called:
a frequency polygon
a pictogram
a time series plot
84. A histogram is a graphical device that is commonly used to analyze:
time series data
quantitative data
qualitative data
3/18/2019 1:44 PM
85. A common rule of thumb in constructing a relative frequency histogram is to use:
less than 5 classes
more than 10 classes
between 5 and 12 classes
any number of classes
at least 10 classes
86. Which of the following is not recommended when constructing a relative frequency histogram?
equal width classes
mutually exclusive classes
open-ended classes
3/18/2019 1:45 PM
87. A histogram is usually used to display which of the following characteristics for a quantitative variable?
the shape of the distribution
the spread or variability in the data
the approximate center of the data
the spread or variability in the data and the approximate center of the data
88. A bar chart is used to display a:
continuous variable
qualitative variable
quantitative variable
discrete variable
89. Which of the following statements is false?
A bar chart and histogram can be used interchangeably.
The bars on a bar chart have the same width.
It is possible to construct a dotplot for quantitative data.
There are gaps between the bars in a bar chart.
3/18/2019 1:48 PM
90. One of the differences between a histogram and bar chart is:
that the bar chart does have gaps between the bars and the histogram does not
that the histogram is used to display the distribution of quantitative data and the bar chart is used to display qualitative data
that the bars of the bar chart can be reordered and the bars of the histogram cannot
3/19/2019 1:47 AM
91. The stem and leaf plot is used to display the distribution of:
two quantitative variables on the same chart
3/19/2019 1:49 AM
92. If the manager of a grocery store wishes to display the sales trend, the most effective type of graph will be:
93. The owner of an Italian restaurant would like to see a graphical display of the number of customers that the restaurant serves. The following data are the average number of customers served each day for the last 12 months.
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Average
180
177
160
154
163
185
165
150
179
240
256
Construct a line graph.Explain what the graph tells us.________________________________________________________
The restaurant serves the most customers in November and December, which may be because of the holiday season. It also has a peak in mid-summer and dips in the spring and fall.
3/28/2019 8:32 AM
94. A math teacher would like to present the midterm results to her class in a way that shows the overall spread of the data. The 25 test scores for the midterm are listed below.
a. Construct a dotplot.
45 78 62 98 50 61 91 89 57 64 77 69 82 73 70 73 79 80 68 72 62 65 78 50 95
b. Explain what the plot tells us.
________________________________________________________
The points are fairly evenly distributed between 45 and 98, with most scores between 60 and 80.
3/28/2019 8:44 AM
95. The librarian of a small community library has compiled the number of people who visited the library and the respective number of checked-out books, and created the line chart shown below:Interpret the chart, where the solid line is the number of visitors and the dashed line is the number of books checked-out.________________________________________________________
The two lines track each other. This means as the number of visitors increase (or decrease) the number of books checked out increases (or decreases).
96. A limnologist is studying a Minnesota lake in October. He records the temperatures in °C for surface water taken every other day at noon. The data are shown below.8.5 8.1 7.9 9.0 7.7 7.3 7.1 6.8 9.26.8 6.3 7.0 6.5 5.7 5.9 4.9 4.2 6.9a. Construct a stem and leaf plot to display the distribution of the data.
Stem
Leaf
4
_________
5
7
8
9
b. Would you describe the distribution of the data as symmetric, skewed to the right or skewed to the left?______________c. Explain.________________________________________________________
2, 9; 7, 9; 3, 5, 8, 8, 9; 0, 1, 3, 7, 9; 1, 5; 0, 2; Symmetric; The distribution seems to be symmetric since the left and right sides of the distribution, when divided at the middle value, form mirror images.
97. The following data represents the number of pages of notes per lecture taken by a student in a beginning statistics course.
1 5 2 6 2 3 3 4 4 4 5
5 5 5 5 5 6 6 6 6 6 6
6 6 5 6 4 5 6
a. Construct a dotplot to describe the data.
b. Would you describe the distribution of the data as symmetric, skewed to the right or skewed to the left?
c. Explain.
Skewed left; The distribution of the data is skewed to the left since the distribution contains few small measurements at the left side and many large measurements at the right side.
3/28/2019 8:51 AM
98. A neighborhood ice cream vendor would like to see if there is a relationship between day of the week and the number of children buying ice cream from her. The following data represent the number of children buying ice cream on each of the seven days of a particular week:
Day
Mo
Tu
We
Th
Fr
Sa
Su
Frequency
3
2
a. Construct a line chart to describe the data.
b. Is there any apparent trend in the data?
The number of children buying ice cream decreases from Monday to midweek, Wednesday, then increases to a maximum on Sunday.
3/29/2019 4:13 AM
99. A high school volleyball coach has summarized the wins, losses, and ties of her team for the past 4 years in the following stacked bar chart. Interpret the chart.
The team's best year was 2001 and their worst was 1998.
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