,MATH 110 Module 2 Exam - Introduction to
Statistics Portage Learning - Latest (26/27)
1. A researcher organizes a dataset of 150 observations into a frequency table with 8 classes. What is
the primary purpose of constructing this frequency distribution?
A) To identify outliers in the raw data
B) To summarize and present the data in a compact, interpretable form
C) To calculate the exact mean of the original dataset
D) To determine the sample size needed for the study
Correct Answer: B) To summarize and present the data in a compact, interpretable form
Rationale: The primary purpose of a frequency distribution is to organize raw data into a compact
summary that reveals patterns, such as shape and spread. While outliers may become apparent, the
main goal is summarization. Calculating the mean is a separate step, and sample size is determined
before data collection.
2. In a frequency distribution table, which column represents the proportion of observations falling
into each class, expressed as a fraction of the total?
A) Frequency
B) Cumulative frequency
C) Relative frequency
D) Class midpoint
Correct Answer: C) Relative frequency
Rationale: Relative frequency is calculated by dividing each class frequency by the total number of
observations. Frequency is the raw count, cumulative frequency is the running total, and class
midpoint is the average of the class boundaries.
,3. A teacher records the number of students who scored in each grade interval on a test. If the interval
"70–79" has a frequency of 12 and the total number of students is 60, what is the relative frequency
for this interval?
A) 0.12
B) 0.20
C) 12
D) 0.80
Correct Answer: B) 0.20
Rationale: Relative frequency is the class frequency divided by the total frequency: 12/60 = 0.20.
Options A (0.12) and C (12) are incorrect; 0.12 is 12% expressed as a decimal incorrectly, and 12 is the
raw frequency.
4. A researcher constructs a frequency distribution for age data with class boundaries of 20 to <30, 30
to <40, and 40 to <50. Which measure is most appropriate for comparing the relative concentration of
data across these classes?
A) Class width
B) Relative frequency
C) Cumulative frequency
D) Class midpoint
Correct Answer: B) Relative frequency
Rationale: Relative frequency standardizes class frequencies by the total, enabling direct comparison
across classes of different sizes or samples. Class width describes intervals, cumulative frequency
shows totals up to a point, and class midpoint is the center value.
5. A dataset of 200 observations is summarized in a frequency table. The sum of all relative
frequencies in the table must equal:
A) 100
B) 200
, C) 1.0
D) The number of classes
Correct Answer: C) 1.0
Rationale: Relative frequencies represent proportions of the total. The sum of all relative frequencies
across all classes must equal 1.0 (or 100% when expressed as a percentage). The sum of raw
frequencies equals the total sample size (200), not the relative frequencies.
6. A bar chart and a histogram are both graphical tools for displaying data. What is the fundamental
difference between them?
A) Bar charts display frequencies; histograms display relative frequencies
B) Bar charts are used for categorical data; histograms are used for quantitative data
C) Bar charts have gaps between bars; histograms have no gaps
D) Both B and C are correct
Correct Answer: D) Both B and C are correct
Rationale: Bar charts display categorical data with gaps between bars to indicate distinct categories.
Histograms display quantitative data with contiguous bars (no gaps) to show continuous intervals.
Both statements B and C are correct.
7. A researcher wants to display the distribution of students' favorite ice cream flavors (Chocolate,
Vanilla, Strawberry, Mint). Which type of graph is most appropriate?
A) Histogram
B) Frequency polygon
C) Bar chart
D) Stem-and-leaf plot
Correct Answer: C) Bar chart
Statistics Portage Learning - Latest (26/27)
1. A researcher organizes a dataset of 150 observations into a frequency table with 8 classes. What is
the primary purpose of constructing this frequency distribution?
A) To identify outliers in the raw data
B) To summarize and present the data in a compact, interpretable form
C) To calculate the exact mean of the original dataset
D) To determine the sample size needed for the study
Correct Answer: B) To summarize and present the data in a compact, interpretable form
Rationale: The primary purpose of a frequency distribution is to organize raw data into a compact
summary that reveals patterns, such as shape and spread. While outliers may become apparent, the
main goal is summarization. Calculating the mean is a separate step, and sample size is determined
before data collection.
2. In a frequency distribution table, which column represents the proportion of observations falling
into each class, expressed as a fraction of the total?
A) Frequency
B) Cumulative frequency
C) Relative frequency
D) Class midpoint
Correct Answer: C) Relative frequency
Rationale: Relative frequency is calculated by dividing each class frequency by the total number of
observations. Frequency is the raw count, cumulative frequency is the running total, and class
midpoint is the average of the class boundaries.
,3. A teacher records the number of students who scored in each grade interval on a test. If the interval
"70–79" has a frequency of 12 and the total number of students is 60, what is the relative frequency
for this interval?
A) 0.12
B) 0.20
C) 12
D) 0.80
Correct Answer: B) 0.20
Rationale: Relative frequency is the class frequency divided by the total frequency: 12/60 = 0.20.
Options A (0.12) and C (12) are incorrect; 0.12 is 12% expressed as a decimal incorrectly, and 12 is the
raw frequency.
4. A researcher constructs a frequency distribution for age data with class boundaries of 20 to <30, 30
to <40, and 40 to <50. Which measure is most appropriate for comparing the relative concentration of
data across these classes?
A) Class width
B) Relative frequency
C) Cumulative frequency
D) Class midpoint
Correct Answer: B) Relative frequency
Rationale: Relative frequency standardizes class frequencies by the total, enabling direct comparison
across classes of different sizes or samples. Class width describes intervals, cumulative frequency
shows totals up to a point, and class midpoint is the center value.
5. A dataset of 200 observations is summarized in a frequency table. The sum of all relative
frequencies in the table must equal:
A) 100
B) 200
, C) 1.0
D) The number of classes
Correct Answer: C) 1.0
Rationale: Relative frequencies represent proportions of the total. The sum of all relative frequencies
across all classes must equal 1.0 (or 100% when expressed as a percentage). The sum of raw
frequencies equals the total sample size (200), not the relative frequencies.
6. A bar chart and a histogram are both graphical tools for displaying data. What is the fundamental
difference between them?
A) Bar charts display frequencies; histograms display relative frequencies
B) Bar charts are used for categorical data; histograms are used for quantitative data
C) Bar charts have gaps between bars; histograms have no gaps
D) Both B and C are correct
Correct Answer: D) Both B and C are correct
Rationale: Bar charts display categorical data with gaps between bars to indicate distinct categories.
Histograms display quantitative data with contiguous bars (no gaps) to show continuous intervals.
Both statements B and C are correct.
7. A researcher wants to display the distribution of students' favorite ice cream flavors (Chocolate,
Vanilla, Strawberry, Mint). Which type of graph is most appropriate?
A) Histogram
B) Frequency polygon
C) Bar chart
D) Stem-and-leaf plot
Correct Answer: C) Bar chart
