EXST 2201 FINAL EXAM (REVISED) QUESTIONS &
COMPLETE DETAILED SOLUTIONS (NEW
2026/2027 UPDATE)
Module 1: Data Summarization & Distribution Shape
1. Q: Why should you always look at a graph to get shape information
instead of just looking at summary numbers for shape?
A: Graphs contain a lot more detail about shape than summary numbers.
Rationale: A graph can reveal multimodal patterns, gaps, clusters, and
outliers that a single summary number like the mean or standard
deviation would completely mask.
2. Q: How do you find the frequency in a column of data values?
A: The number of times a value occurs in a column of data values.
Rationale: The frequency is the simple count of how many times each
distinct value appears in your dataset.
3. Q: Match the columns in a frequency table with their meaning below.
A: Frequency = The number of times a value occurs; Relative Frequency =
The proportion of times a value occurs; Cumulative Frequency = A partial
sum of the Frequency column; Cumulative Relative Frequency = A partial
sum of the Relative Frequency column.
Rationale: The frequency table builds descriptive statistics step by step:
starting with counts (frequency), proportions (relative frequency), and
then running totals (cumulative frequency and cumulative relative
frequency).
,4. Q: What are the two characteristics you look at to analyze the shape
of a column of data values?
A: Overall shape and exceptions.
Rationale: The "overall shape" identifies general patterns (symmetry,
skewness), while "exceptions" refer to outliers or unusual gaps within the
distribution.
5. Q: What type of graph is most appropriate to display the shape of
qualitative data?
A: A bar chart, where the bars do not touch each other.
Rationale: Qualitative (categorical) data uses separate bars to represent
distinct, unordered categories. The gaps between bars highlight that there
is no natural numerical order.
6. Q: Can any, and all, bar charts be changed into a Pareto chart?
A: Yes, because the categories are not over a real-number-line and can be
rearranged.
Rationale: Since categories are separate and can be ordered by their
frequency, any bar chart can be reorganized into a Pareto chart (bars
sorted from highest to lowest frequency with a cumulative line).
7. Q: What type of graph is most appropriate to display the shape of
discrete data?
A: A histogram where the bars do touch each other.
Rationale: Discrete numerical data occupies distinct values on a number
line. The touching bars in a histogram emphasize continuity along the
numerical scale, even though the data points themselves are individual.
8. Q: What are the key characteristics to look for when analyzing the
shape of a distribution?
, A: The number of peaks (modality), symmetry (or skewness), and the
presence of outliers or gaps.
Rationale: Modality (e.g., unimodal vs. bimodal) and symmetry (skewed
left/right) describe the distribution's fundamental structure, while outliers
indicate exceptional data points that may require investigation.
9. Q: What is a multimodal distribution?
A: A distribution with two or more distinct peaks (modes), suggesting the
data may come from multiple subgroups or processes.
Rationale: A multimodal histogram suggests that your data is likely a
mixture of two or more different populations or conditions.
📋 Module 2: Descriptive Statistics & Measures of Center
10. Q: What are the three most common measures of central tendency?
A: The mean, the median, and the mode.
Rationale: The mean is the arithmetic average, the median is the middle
value, and the mode is the most frequently occurring value. They provide
different perspectives on "typical" values in a dataset.
11. Q: Which measure of central tendency is most resistant to the
influence of outliers?
A: The median.
Rationale: The median is determined by the order of the values and is not
distorted by a few extremely large or small numbers.
12. Q: What is the interquartile range (IQR)?
A: The range between the first quartile (Q1, 25th percentile) and the third
quartile (Q3, 75th percentile).
COMPLETE DETAILED SOLUTIONS (NEW
2026/2027 UPDATE)
Module 1: Data Summarization & Distribution Shape
1. Q: Why should you always look at a graph to get shape information
instead of just looking at summary numbers for shape?
A: Graphs contain a lot more detail about shape than summary numbers.
Rationale: A graph can reveal multimodal patterns, gaps, clusters, and
outliers that a single summary number like the mean or standard
deviation would completely mask.
2. Q: How do you find the frequency in a column of data values?
A: The number of times a value occurs in a column of data values.
Rationale: The frequency is the simple count of how many times each
distinct value appears in your dataset.
3. Q: Match the columns in a frequency table with their meaning below.
A: Frequency = The number of times a value occurs; Relative Frequency =
The proportion of times a value occurs; Cumulative Frequency = A partial
sum of the Frequency column; Cumulative Relative Frequency = A partial
sum of the Relative Frequency column.
Rationale: The frequency table builds descriptive statistics step by step:
starting with counts (frequency), proportions (relative frequency), and
then running totals (cumulative frequency and cumulative relative
frequency).
,4. Q: What are the two characteristics you look at to analyze the shape
of a column of data values?
A: Overall shape and exceptions.
Rationale: The "overall shape" identifies general patterns (symmetry,
skewness), while "exceptions" refer to outliers or unusual gaps within the
distribution.
5. Q: What type of graph is most appropriate to display the shape of
qualitative data?
A: A bar chart, where the bars do not touch each other.
Rationale: Qualitative (categorical) data uses separate bars to represent
distinct, unordered categories. The gaps between bars highlight that there
is no natural numerical order.
6. Q: Can any, and all, bar charts be changed into a Pareto chart?
A: Yes, because the categories are not over a real-number-line and can be
rearranged.
Rationale: Since categories are separate and can be ordered by their
frequency, any bar chart can be reorganized into a Pareto chart (bars
sorted from highest to lowest frequency with a cumulative line).
7. Q: What type of graph is most appropriate to display the shape of
discrete data?
A: A histogram where the bars do touch each other.
Rationale: Discrete numerical data occupies distinct values on a number
line. The touching bars in a histogram emphasize continuity along the
numerical scale, even though the data points themselves are individual.
8. Q: What are the key characteristics to look for when analyzing the
shape of a distribution?
, A: The number of peaks (modality), symmetry (or skewness), and the
presence of outliers or gaps.
Rationale: Modality (e.g., unimodal vs. bimodal) and symmetry (skewed
left/right) describe the distribution's fundamental structure, while outliers
indicate exceptional data points that may require investigation.
9. Q: What is a multimodal distribution?
A: A distribution with two or more distinct peaks (modes), suggesting the
data may come from multiple subgroups or processes.
Rationale: A multimodal histogram suggests that your data is likely a
mixture of two or more different populations or conditions.
📋 Module 2: Descriptive Statistics & Measures of Center
10. Q: What are the three most common measures of central tendency?
A: The mean, the median, and the mode.
Rationale: The mean is the arithmetic average, the median is the middle
value, and the mode is the most frequently occurring value. They provide
different perspectives on "typical" values in a dataset.
11. Q: Which measure of central tendency is most resistant to the
influence of outliers?
A: The median.
Rationale: The median is determined by the order of the values and is not
distorted by a few extremely large or small numbers.
12. Q: What is the interquartile range (IQR)?
A: The range between the first quartile (Q1, 25th percentile) and the third
quartile (Q3, 75th percentile).
