TEST BANK &
SOLUTION MANUAL
FOR ELEMENTARY
STATISTICS
Chapter 1: Introduction to Statistics
1. Which of the following best describes the difference between a population and
a sample?
A. A population is a subset of a sample
B. A population is the complete collection of all individuals or items to be studied,
while a sample is a subset of that population
C. A population is always larger than 1,000 individuals
D. A sample is always randomly selected, while a population is not
Rationale: By definition, a population includes all subjects of interest, while a sample is
a portion of the population selected for study. Size is not the defining factor, and
randomness applies to sampling methods, not the definition of a population.
2. A researcher records the number of cars passing through an intersection each
hour. This variable is:
A. Quantitative discrete
B. Quantitative continuous
,C. Qualitative nominal
D. Qualitative ordinal
Rationale: The number of cars is a countable whole number, making it quantitative
discrete. Continuous data would involve measurements on a scale (e.g., time, weight).
3. Which level of measurement is characterized by data that can be ordered, but
differences between values are not meaningful?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Rationale: Ordinal data can be ranked (e.g., small, medium, large), but the differences
between ranks are not equal or meaningful. Interval and ratio data have meaningful
differences.
4. A study where the researcher observes and measures characteristics without
modifying the subjects is called:
A. An experiment
B. An observational study
C. A simulation
D. A census
Rationale: In an observational study, researchers observe and measure without
controlling or manipulating the subjects. In an experiment, treatments are applied.
5. Which sampling method involves dividing the population into subgroups and
randomly selecting from each subgroup?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Convenience sampling
Rationale: Stratified sampling divides the population into strata (subgroups) and
randomly samples from each. Cluster sampling selects entire groups; systematic
sampling uses a rule (e.g., every kth item).
6. A researcher surveys 500 people by selecting every 10th person from a list. This
is an example of:
,A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Cluster sampling
Rationale: Selecting every kth individual from a list is the definition of systematic
sampling.
7. Which of the following is an example of a parameter?
A. The mean height of 50 randomly selected students
B. The mean height of all students in a university
C. The proportion of defective items in a sample
D. The standard deviation of a sample
Rationale: A parameter is a numerical measure describing a population. Statistics
describe samples.
Chapter 2: Summarizing and Graphing Data
8. In a frequency distribution, the class width is:
A. The number of classes
B. The difference between consecutive lower class limits
C. The highest frequency minus the lowest frequency
D. The total number of observations
Rationale: Class width is the difference between consecutive lower class limits (or upper
class limits). It determines the span of each class.
9. A histogram differs from a bar chart primarily because:
A. A histogram is used for quantitative data with no gaps between bars, while a
bar chart is used for categorical data with gaps
B. A histogram is used for categorical data
C. A bar chart shows frequencies, while a histogram does not
D. There is no difference between them
Rationale: Histograms display quantitative data with contiguous bars, while bar charts
display categorical data with separated bars.
10. A distribution is skewed to the right when:
, A. The left tail is longer than the right tail
B. The right tail is longer than the left tail
C. The mean is less than the median
D. The distribution is perfectly symmetric
Answer: B
Rationale: Right-skewed (positive skew) distributions have a longer right tail. The mean
is typically greater than the median.
11. In a symmetric distribution, which of the following is true?
A. The mean is greater than the median
B. The mean is less than the median
C. The mean, median, and mode are approximately equal
D. The mode is always zero
Rationale: In a perfectly symmetric distribution, the mean, median, and mode coincide
at the center.
12. A dotplot is most useful for:
A. Displaying small data sets to show the shape and distribution
B. Large data sets with thousands of values
C. Categorical data only
D. Showing cumulative frequencies
Rationale: Dotplots work best for small data sets where each value can be represented
by a dot, revealing shape, center, and spread.
13. A stemplot (stem-and-leaf plot) has the advantage of:
A. Being easier to construct than a histogram
B. Retaining the original data values while showing distribution shape
C. Being useful only for large data sets
D. Eliminating the need for sorting data
Rationale: Stemplots preserve individual data values while displaying the distribution,
unlike histograms which group data.
SOLUTION MANUAL
FOR ELEMENTARY
STATISTICS
Chapter 1: Introduction to Statistics
1. Which of the following best describes the difference between a population and
a sample?
A. A population is a subset of a sample
B. A population is the complete collection of all individuals or items to be studied,
while a sample is a subset of that population
C. A population is always larger than 1,000 individuals
D. A sample is always randomly selected, while a population is not
Rationale: By definition, a population includes all subjects of interest, while a sample is
a portion of the population selected for study. Size is not the defining factor, and
randomness applies to sampling methods, not the definition of a population.
2. A researcher records the number of cars passing through an intersection each
hour. This variable is:
A. Quantitative discrete
B. Quantitative continuous
,C. Qualitative nominal
D. Qualitative ordinal
Rationale: The number of cars is a countable whole number, making it quantitative
discrete. Continuous data would involve measurements on a scale (e.g., time, weight).
3. Which level of measurement is characterized by data that can be ordered, but
differences between values are not meaningful?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Rationale: Ordinal data can be ranked (e.g., small, medium, large), but the differences
between ranks are not equal or meaningful. Interval and ratio data have meaningful
differences.
4. A study where the researcher observes and measures characteristics without
modifying the subjects is called:
A. An experiment
B. An observational study
C. A simulation
D. A census
Rationale: In an observational study, researchers observe and measure without
controlling or manipulating the subjects. In an experiment, treatments are applied.
5. Which sampling method involves dividing the population into subgroups and
randomly selecting from each subgroup?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Convenience sampling
Rationale: Stratified sampling divides the population into strata (subgroups) and
randomly samples from each. Cluster sampling selects entire groups; systematic
sampling uses a rule (e.g., every kth item).
6. A researcher surveys 500 people by selecting every 10th person from a list. This
is an example of:
,A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Cluster sampling
Rationale: Selecting every kth individual from a list is the definition of systematic
sampling.
7. Which of the following is an example of a parameter?
A. The mean height of 50 randomly selected students
B. The mean height of all students in a university
C. The proportion of defective items in a sample
D. The standard deviation of a sample
Rationale: A parameter is a numerical measure describing a population. Statistics
describe samples.
Chapter 2: Summarizing and Graphing Data
8. In a frequency distribution, the class width is:
A. The number of classes
B. The difference between consecutive lower class limits
C. The highest frequency minus the lowest frequency
D. The total number of observations
Rationale: Class width is the difference between consecutive lower class limits (or upper
class limits). It determines the span of each class.
9. A histogram differs from a bar chart primarily because:
A. A histogram is used for quantitative data with no gaps between bars, while a
bar chart is used for categorical data with gaps
B. A histogram is used for categorical data
C. A bar chart shows frequencies, while a histogram does not
D. There is no difference between them
Rationale: Histograms display quantitative data with contiguous bars, while bar charts
display categorical data with separated bars.
10. A distribution is skewed to the right when:
, A. The left tail is longer than the right tail
B. The right tail is longer than the left tail
C. The mean is less than the median
D. The distribution is perfectly symmetric
Answer: B
Rationale: Right-skewed (positive skew) distributions have a longer right tail. The mean
is typically greater than the median.
11. In a symmetric distribution, which of the following is true?
A. The mean is greater than the median
B. The mean is less than the median
C. The mean, median, and mode are approximately equal
D. The mode is always zero
Rationale: In a perfectly symmetric distribution, the mean, median, and mode coincide
at the center.
12. A dotplot is most useful for:
A. Displaying small data sets to show the shape and distribution
B. Large data sets with thousands of values
C. Categorical data only
D. Showing cumulative frequencies
Rationale: Dotplots work best for small data sets where each value can be represented
by a dot, revealing shape, center, and spread.
13. A stemplot (stem-and-leaf plot) has the advantage of:
A. Being easier to construct than a histogram
B. Retaining the original data values while showing distribution shape
C. Being useful only for large data sets
D. Eliminating the need for sorting data
Rationale: Stemplots preserve individual data values while displaying the distribution,
unlike histograms which group data.
