OSC 2030 CHAPTERS 1-4 | THE DEFINITIVE 200-QUESTION
COMPREHENSIVE FINAL EXAM BANK WITH VERIFIED ANSWERS,
RANDOMIZED OPTIONS, AND DETAILED RATIONALES
1. A frequency distribution is a table that summarizes data by showing
the:
A. Percentage of data values falling below the mean.
B. Number of observations falling into each class interval.
C. Cumulative total of all data values.
D. Rank order of data from smallest to largest.
Correct Answer: B
Rationale: A frequency distribution groups data into classes and displays
the count (frequency) of observations in each class. It does not show
percentages below the mean, cumulative totals, or rank order directly.
2. Which of the following is a key characteristic of a frequency
distribution?
A. It always has exactly 10 classes.
B. Classes must be of unequal width.
C. Each data value belongs to exactly one class.
D. It only applies to qualitative data.
Correct Answer: C
Rationale: In a proper frequency distribution, classes are mutually
exclusive, meaning each observation falls into one and only one class.
Class width can vary, and the number of classes is not fixed at 10.
,3. The recommended number of classes for a frequency distribution
with 500 data values is:
A. Exactly 20.
B. Between 5 and 20.
C. At least 25.
D. Equal to 125.
Correct Answer: B
Rationale: The rule of thumb for constructing a frequency distribution is
to use between 5 and 20 classes, regardless of the exact sample size, to
provide a clear summary without losing detail.
4. A frequency distribution using 12 classes with equal width will have
a class width equal to:
A. (Range) / 12.
B. (Mean) / 12.
C. (Standard deviation) / 12.
D. (Median) / 12.
Correct Answer: A
Rationale: Class width is calculated as the range (maximum minus
minimum) divided by the number of classes. This ensures equal
intervals across the data.
5. A relative frequency distribution shows the:
A. Actual count in each class.
B. Proportion or percentage of observations in each class.
C. Cumulative total of frequencies.
D. Midpoint of each class.
Correct Answer: B
Rationale: Relative frequency is the class frequency divided by total
,observations, giving the proportion or percentage. It does not show
actual counts, cumulative totals, or midpoints.
6. A cumulative frequency distribution is used to determine:
A. The number of observations below a certain value.
B. The class width.
C. The mean of the data.
D. The mode of the data.
Correct Answer: A
Rationale: Cumulative frequency adds frequencies from the lowest class
upward, showing how many observations fall below the upper
boundary of each class. It does not determine class width, mean, or
mode.
7. A histogram is most appropriate for displaying:
A. The relationship between two variables.
B. The distribution of a single quantitative variable.
C. The proportion of categories in a qualitative variable.
D. Trends over time.
Correct Answer: B
Rationale: A histogram is a graphical representation of a frequency
distribution for quantitative data, showing the shape and spread of the
data. It is not used for two variables, qualitative categories, or time
trends.
8. A bar chart and a histogram differ in that:
A. A histogram has gaps between bars, while a bar chart does not.
B. A bar chart is used for quantitative data, and a histogram for
qualitative.
C. A histogram has no gaps between bars, while a bar chart has gaps.
, D. They are identical in construction.
Correct Answer: C
Rationale: A histogram uses contiguous bars (no gaps) to represent
quantitative data, while a bar chart has gaps between bars to
distinguish qualitative categories. The reverse of A and B is false.
9. A stem-and-leaf display retains the original data values while
showing the distribution. This is an advantage over a histogram
because:
A. It is easier to construct.
B. It preserves individual data points.
C. It always has fewer classes.
D. It can only be used for small samples.
Correct Answer: B
Rationale: Unlike a histogram, a stem-and-leaf plot shows each data
value individually, preserving the actual observations while still
displaying the distribution shape.
10. A frequency polygon is constructed by:
A. Connecting the midpoints of each class at the class frequency.
B. Connecting the upper class boundaries.
C. Plotting cumulative frequencies.
D. Using bars of equal width.
Correct Answer: A
Rationale: A frequency polygon uses points representing class
frequencies plotted at class midpoints, then connects them with
straight lines. It does not use boundaries or cumulative frequencies.
11. An ogive is a graph that displays:
A. Relative frequencies.
COMPREHENSIVE FINAL EXAM BANK WITH VERIFIED ANSWERS,
RANDOMIZED OPTIONS, AND DETAILED RATIONALES
1. A frequency distribution is a table that summarizes data by showing
the:
A. Percentage of data values falling below the mean.
B. Number of observations falling into each class interval.
C. Cumulative total of all data values.
D. Rank order of data from smallest to largest.
Correct Answer: B
Rationale: A frequency distribution groups data into classes and displays
the count (frequency) of observations in each class. It does not show
percentages below the mean, cumulative totals, or rank order directly.
2. Which of the following is a key characteristic of a frequency
distribution?
A. It always has exactly 10 classes.
B. Classes must be of unequal width.
C. Each data value belongs to exactly one class.
D. It only applies to qualitative data.
Correct Answer: C
Rationale: In a proper frequency distribution, classes are mutually
exclusive, meaning each observation falls into one and only one class.
Class width can vary, and the number of classes is not fixed at 10.
,3. The recommended number of classes for a frequency distribution
with 500 data values is:
A. Exactly 20.
B. Between 5 and 20.
C. At least 25.
D. Equal to 125.
Correct Answer: B
Rationale: The rule of thumb for constructing a frequency distribution is
to use between 5 and 20 classes, regardless of the exact sample size, to
provide a clear summary without losing detail.
4. A frequency distribution using 12 classes with equal width will have
a class width equal to:
A. (Range) / 12.
B. (Mean) / 12.
C. (Standard deviation) / 12.
D. (Median) / 12.
Correct Answer: A
Rationale: Class width is calculated as the range (maximum minus
minimum) divided by the number of classes. This ensures equal
intervals across the data.
5. A relative frequency distribution shows the:
A. Actual count in each class.
B. Proportion or percentage of observations in each class.
C. Cumulative total of frequencies.
D. Midpoint of each class.
Correct Answer: B
Rationale: Relative frequency is the class frequency divided by total
,observations, giving the proportion or percentage. It does not show
actual counts, cumulative totals, or midpoints.
6. A cumulative frequency distribution is used to determine:
A. The number of observations below a certain value.
B. The class width.
C. The mean of the data.
D. The mode of the data.
Correct Answer: A
Rationale: Cumulative frequency adds frequencies from the lowest class
upward, showing how many observations fall below the upper
boundary of each class. It does not determine class width, mean, or
mode.
7. A histogram is most appropriate for displaying:
A. The relationship between two variables.
B. The distribution of a single quantitative variable.
C. The proportion of categories in a qualitative variable.
D. Trends over time.
Correct Answer: B
Rationale: A histogram is a graphical representation of a frequency
distribution for quantitative data, showing the shape and spread of the
data. It is not used for two variables, qualitative categories, or time
trends.
8. A bar chart and a histogram differ in that:
A. A histogram has gaps between bars, while a bar chart does not.
B. A bar chart is used for quantitative data, and a histogram for
qualitative.
C. A histogram has no gaps between bars, while a bar chart has gaps.
, D. They are identical in construction.
Correct Answer: C
Rationale: A histogram uses contiguous bars (no gaps) to represent
quantitative data, while a bar chart has gaps between bars to
distinguish qualitative categories. The reverse of A and B is false.
9. A stem-and-leaf display retains the original data values while
showing the distribution. This is an advantage over a histogram
because:
A. It is easier to construct.
B. It preserves individual data points.
C. It always has fewer classes.
D. It can only be used for small samples.
Correct Answer: B
Rationale: Unlike a histogram, a stem-and-leaf plot shows each data
value individually, preserving the actual observations while still
displaying the distribution shape.
10. A frequency polygon is constructed by:
A. Connecting the midpoints of each class at the class frequency.
B. Connecting the upper class boundaries.
C. Plotting cumulative frequencies.
D. Using bars of equal width.
Correct Answer: A
Rationale: A frequency polygon uses points representing class
frequencies plotted at class midpoints, then connects them with
straight lines. It does not use boundaries or cumulative frequencies.
11. An ogive is a graph that displays:
A. Relative frequencies.
