1.1 1) Statistics refers to numerical facts such as the age of a student or the income of a
family.
2) Statistics refers to the field or discipline of study. Statistics is a group of methods
used to collect, analyze, present, and interpret data and to make decisions.
1.2 Descriptive statistics consists of methods that help us organize, display, and
describe data using tables, graphs, and summary measures. Inferential statistics
consists of methods that use sample results to help make decisions or predictions
about a population.
1.3 a. This is an example of inferential statistics because a poll was taken using a sample
of adults and based on the results, conclusions are inferred with a certain margin
of error.
b. This is an example of descriptive statistics because information was gathered and
tabulated, but no inference was made to a larger population.
Section 1.2
1.4 An element is a specific subject or object about which the information is collected.
A variable is a characteristic under study that assumes different values for
different elements. An observation is the value of a variable for a single element.
A data set is a collection of observations on one or more variables.
1.5 With reference to this table, we have the following definitions:
• Member: Each cause of death included in the table
• Variable: The number of deaths
• Measurement: The number of deaths from each cause of death
• Data set: Collection of the number of deaths from each cause of death listed in the
table
1.6 a. Number of deaths
b. Nine
c. Nine (causes of death)
1
,2 Chapter 1
Section 1.3
1.7 a. A quantitative variable is a variable that can be measured numerically.
b. A variable that cannot assume a numeric value but can be classified into two or
more nonnumeric categories is called a qualitative variable.
c. A discrete variable is a variable whose values are countable.
d. A variable that can assume any numerical value over a certain interval or
intervals is called a continuous variable.
e. Data collected on a quantitative variable is called quantitative data.
f. Qualitative data is data collected on a qualitative variable.
1.8 a. Quantitative b. Quantitative
c. Qualitative d. Qualitative
e. Quantitative
1.9 a. Continuous b. Continuous
c. Continuous d. Discrete
1.10 a. The qualitative variables are: do they own a house, have they taken a vacation
during the past year, are they happy with their financial situation
b. The quantitative variables are: age of oldest person in family, number of family
members, number of males in the family, number of females in the family, income
of family, and amount of monthly mortgage or rent
c. The discrete variables are number of family members, number of males in the
family and number of females in the family
d. The continuous variables are: age of oldest family member, income of family, and
amount of monthly mortgage or rent
, Chapter 1 3
Section 1.4
1.11 Data collected on different elements at the same point in time or for the same
period of time are called cross-section data. Total sales for the 2019 Christmas
season at 10 stores in a particular mall is an example of cross-section data.
Data collected on the same element for the same variable at different points in
time or for different periods of time are called time-series data. Total sales for one
particular store for the Christmas season for the years 2009 to 2019 is an example
of time-series data.
1.12 a. Time-series data
b. Time-series data
c. Cross-section data
d. Cross-section data
Section 1.5
1.13 A population is the collection of all elements whose characteristics are being
studied.
A sample is a portion of the population selected for study.
A representative sample is a sample that represents the characteristics of the
population as closely as possible.
Sampling with replacement refers to a sampling procedure in which the item selected
at each selection is put back in the population before the next item is drawn.
Sampling without replacement is a sampling procedure in which the item selected
at each selection is not replaced in the population.
1.14 Consider a jar of marbles containing 5 blue, 3 red, and 2 yellow marbles.
Suppose we randomly select one marble from the jar and record the color. If we
put this marble back in the jar before we randomly select a second marble, this is
an example of sampling with replacement. If we put the first marble aside and
randomly select the second marble from the 9 marbles remaining in the jar, this is
an example of sampling without replacement.
1.15 A census is a survey that includes every member of the population.
A survey based on a portion of the population is called a sample survey.
A sample survey is preferred over a census for the following reasons:
1) Conducting a census is very expensive because the size of the population is
often very large.
2) Conducting a census is very time consuming.
3) In many cases it is impossible to identify each element of the target
population.
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1.16 a. A sample drawn in such a way that each member of the population has some
chance of being selected in the sample is called a random sample.
b. A sample in which some members of the population may have no chance of being
selected is called a nonrandom sample.
c. A convenience sample is a sample in which the most accessible members of the
population are selected.
d. A judgment sample is a sample in which members of a population are selected
based on the judgment and prior knowledge of an expert.
e. A quota sample is a sample selected in such a way that each group or
subpopulation is represented in the sample in exactly the same proportion as in
the target population.
1.17 a. A sampling technique under which each sample of the same size has the same
probability of being selected is called a simple random sample.
b. In systematic random sampling, we first randomly select one member from the
first k units. Then, every kth member, starting with the first selected member, is
included in the sample.
c. In a stratified random sample, we first divide the population into subpopulations
which are called strata. Then, one sample is selected from each of these strata.
The collection of all samples from all strata gives the stratified random sample.
d. In cluster sampling, the whole population is divided into (geographical) groups
called clusters. Each cluster is representative of the population. Then, a random
sample of clusters is selected. Finally, a random sample of elements of each of the
selected clusters is selected.
1.18 Simple random sample
1.19 a. Population b. Sample
c. Population d. Population
e. Sample
1.20 a. This is a nonrandom sample since students in the university who were not in her
statistics class had no chance of being included in the sample.
b. This is a convenience sample since students in her class were the most accessible
members of the population.
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