WGU C955 Applied Probability & Statistics ACTUAL
FINAL EXAM PRACTICE 2026/2027 | Verified
Questions and Answers | Aligned to WGU
Competencies | Grade A Target | Pass Guaranteed
SECTION 1: Data Fundamentals & Descriptive Statistics (Questions 1-15)
Q1: A hospital quality improvement team is analyzing patient satisfaction survey data. The
survey asks patients to rate their experience as "Poor," "Fair," "Good," "Very Good," or
"Excellent." What level of measurement does this variable represent?
A. Nominal - categories without inherent order B. Ordinal - categories with meaningful order
but unequal intervals [CORRECT] C. Interval - ordered categories with equal intervals but no true
zero D. Ratio - ordered categories with equal intervals and a true zero
Correct Answer: B
Rationale: Patient satisfaction ratings represent ordinal measurement because: (1) the
categories have a clear, meaningful order (Poor < Fair < Good < Very Good < Excellent), but (2)
the intervals between categories are not necessarily equal—we cannot assume the difference
between "Poor" and "Fair" equals the difference between "Good" and "Very Good."
• Option A (Nominal) is incorrect because the categories DO have a natural order (unlike,
say, blood types or gender).
• Option C (Interval) is incorrect because we cannot quantify the exact difference
between ratings numerically.
• Option D (Ratio) is incorrect because there is no true zero point (a rating of zero would
be undefined, and ratios like "Excellent is twice as good as Fair" are meaningless).
In healthcare analytics, recognizing ordinal data is crucial because calculating means is
inappropriate—medians and modes are preferred for central tendency.
,Q2: A manufacturing company tracks the temperature of industrial ovens in degrees Celsius.
The data shows a reading of 0°C when the oven is off. What level of measurement is oven
temperature?
A. Nominal B. Ordinal C. Interval [CORRECT] D. Ratio
Correct Answer: C
Rationale: Temperature in Celsius represents interval measurement because: (1) values are
ordered with equal intervals (the difference between 10°C and 20°C equals the difference
between 30°C and 40°C), but (2) 0°C does not represent the complete absence of
temperature—it is an arbitrary point (the freezing point of water), not a true zero. Therefore,
ratios are meaningless (20°C is not "twice as hot" as 10°C).
• Option D (Ratio) is incorrect because 0°C is not a true zero (absolute zero is -273.15°C).
Only Kelvin temperature is ratio-level.
• Options A and B are incorrect because temperature has both order and equal intervals.
This distinction matters in quality control: while we can calculate means and standard deviations
for interval data, we cannot make ratio statements about temperature differences.
Q3: A retail analyst is examining the distribution of daily sales transactions. The dataset
contains: 120, 145, 132, 128, 950, 138, 142, 135, 130, 140 (in dollars). Which measure of central
tendency best represents "typical" daily sales?
A. Mean = $216.00 B. Median = $136.50 [CORRECT] C. Mode = $120 D. Range = $830
Correct Answer: B
Rationale: The median ($136.50) is the best measure because the dataset contains an extreme
outlier ($950, likely a bulk purchase or data entry error). The median is resistant to outliers,
while the mean is pulled upward by the extreme value. Calculating the median: ordered data is
120, 128, 130, 132, 135, 138, 140, 142, 145, 950. With 10 observations, the median is the
average of the 5th and 6th values: (135 + 138)/2 = $136.50.
• Option A (Mean) is calculated as $2,160/10 = $216, but this overestimates typical daily
sales due to the outlier's influence.
• Option C (Mode) is incorrect—there is no mode (all values are unique), and $120 is
simply the minimum value.
• Option D (Range) is a measure of spread, not central tendency.
,In business analytics, understanding when outliers distort the mean is essential for accurate
reporting and forecasting.
Q4: Given the dataset: 12, 15, 18, 22, 25, 28, 32, 35, 100, what is the interquartile range (IQR)?
A. 15 B. 17 [CORRECT] C. 20 D. 88
Correct Answer: B
Rationale: To calculate IQR = Q3 - Q1:
1. Order data: Already ordered: 12, 15, 18, 22, 25, 28, 32, 35, 100 (n=9)
2. Find median (Q2): The 5th value = 25
3. Find Q1 (median of lower half): Lower half = 12, 15, 18, 22. Q1 = (15 + 18)/2 = 16.5
4. Find Q3 (median of upper half): Upper half = 28, 32, 35, 100. Q3 = (32 + 35)/2 = 33.5
5. IQR = 33.5 - 16.5 = 17
• Option A (15) results from incorrectly using (22 - 18) or other incorrect quartile
calculations.
• Option C (20) might result from (35 - 15), confusing quartiles with raw data positions.
• Option D (88) is the full range (100 - 12), not the IQR.
The IQR represents the spread of the middle 50% of data, making it robust to outliers like the
value 100 in this dataset.
Q5: A box plot displays the following five-number summary for employee salaries (in
thousands): Min = $32K, Q1 = $45K, Median = $58K, Q3 = $72K, Max = $95K. Which statement
accurately interprets this distribution?
A. 50% of employees earn between $32K and $58K B. 75% of employees earn more than $72K
C. The middle 50% of salaries span $27K [CORRECT] D. The distribution is symmetric with no
skew
Correct Answer: C
Rationale: The IQR (middle 50%) = Q3 - Q1 = $72K - $45K = $27K. This correctly interprets the
box portion of the box plot.
, • Option A is incorrect—50% of employees earn below the median ($58K), not between
min and median. The lower 50% spans $32K to $58K ($26K range).
• Option B is reversed—75% of employees earn LESS than $72K (Q3 represents the 75th
percentile).
• Option D is incorrect—the distribution shows right skew: the upper whisker ($95K - $72K
= $23K) is longer than the lower whisker ($45K - $32K = $13K), and the median is closer
to Q1 than Q3.
Box plots efficiently display skewness and outliers, crucial for HR analytics and compensation
analysis.
Q6: A marketing team surveys 500 customers about brand preference (Brand A, B, or C). To
display the frequency distribution effectively, which graphical method is most appropriate?
A. Histogram B. Scatterplot C. Bar chart [CORRECT] D. Box plot
Correct Answer: C
Rationale: A bar chart is appropriate for displaying categorical data (nominal level: Brand A, B,
C). Bars are separated to emphasize distinct categories, and heights represent frequencies or
percentages.
• Option A (Histogram) is for continuous quantitative data where bars touch to show the
continuous scale.
• Option B (Scatterplot) displays the relationship between two quantitative variables.
• Option D (Box plot) summarizes distribution of a single quantitative variable.
In business reporting, choosing the correct graph prevents misinterpretation—using a histogram
for categorical data is a common error that implies false continuity between categories.
Q7: A dataset has a mean of 50 and a standard deviation of 10. Using the empirical rule,
approximately what percentage of data falls between 30 and 70?
A. 68% B. 95% [CORRECT] C. 99.7% D. 100%
Correct Answer: B
Rationale: The empirical rule (68-95-99.7 rule) for normal distributions states:
FINAL EXAM PRACTICE 2026/2027 | Verified
Questions and Answers | Aligned to WGU
Competencies | Grade A Target | Pass Guaranteed
SECTION 1: Data Fundamentals & Descriptive Statistics (Questions 1-15)
Q1: A hospital quality improvement team is analyzing patient satisfaction survey data. The
survey asks patients to rate their experience as "Poor," "Fair," "Good," "Very Good," or
"Excellent." What level of measurement does this variable represent?
A. Nominal - categories without inherent order B. Ordinal - categories with meaningful order
but unequal intervals [CORRECT] C. Interval - ordered categories with equal intervals but no true
zero D. Ratio - ordered categories with equal intervals and a true zero
Correct Answer: B
Rationale: Patient satisfaction ratings represent ordinal measurement because: (1) the
categories have a clear, meaningful order (Poor < Fair < Good < Very Good < Excellent), but (2)
the intervals between categories are not necessarily equal—we cannot assume the difference
between "Poor" and "Fair" equals the difference between "Good" and "Very Good."
• Option A (Nominal) is incorrect because the categories DO have a natural order (unlike,
say, blood types or gender).
• Option C (Interval) is incorrect because we cannot quantify the exact difference
between ratings numerically.
• Option D (Ratio) is incorrect because there is no true zero point (a rating of zero would
be undefined, and ratios like "Excellent is twice as good as Fair" are meaningless).
In healthcare analytics, recognizing ordinal data is crucial because calculating means is
inappropriate—medians and modes are preferred for central tendency.
,Q2: A manufacturing company tracks the temperature of industrial ovens in degrees Celsius.
The data shows a reading of 0°C when the oven is off. What level of measurement is oven
temperature?
A. Nominal B. Ordinal C. Interval [CORRECT] D. Ratio
Correct Answer: C
Rationale: Temperature in Celsius represents interval measurement because: (1) values are
ordered with equal intervals (the difference between 10°C and 20°C equals the difference
between 30°C and 40°C), but (2) 0°C does not represent the complete absence of
temperature—it is an arbitrary point (the freezing point of water), not a true zero. Therefore,
ratios are meaningless (20°C is not "twice as hot" as 10°C).
• Option D (Ratio) is incorrect because 0°C is not a true zero (absolute zero is -273.15°C).
Only Kelvin temperature is ratio-level.
• Options A and B are incorrect because temperature has both order and equal intervals.
This distinction matters in quality control: while we can calculate means and standard deviations
for interval data, we cannot make ratio statements about temperature differences.
Q3: A retail analyst is examining the distribution of daily sales transactions. The dataset
contains: 120, 145, 132, 128, 950, 138, 142, 135, 130, 140 (in dollars). Which measure of central
tendency best represents "typical" daily sales?
A. Mean = $216.00 B. Median = $136.50 [CORRECT] C. Mode = $120 D. Range = $830
Correct Answer: B
Rationale: The median ($136.50) is the best measure because the dataset contains an extreme
outlier ($950, likely a bulk purchase or data entry error). The median is resistant to outliers,
while the mean is pulled upward by the extreme value. Calculating the median: ordered data is
120, 128, 130, 132, 135, 138, 140, 142, 145, 950. With 10 observations, the median is the
average of the 5th and 6th values: (135 + 138)/2 = $136.50.
• Option A (Mean) is calculated as $2,160/10 = $216, but this overestimates typical daily
sales due to the outlier's influence.
• Option C (Mode) is incorrect—there is no mode (all values are unique), and $120 is
simply the minimum value.
• Option D (Range) is a measure of spread, not central tendency.
,In business analytics, understanding when outliers distort the mean is essential for accurate
reporting and forecasting.
Q4: Given the dataset: 12, 15, 18, 22, 25, 28, 32, 35, 100, what is the interquartile range (IQR)?
A. 15 B. 17 [CORRECT] C. 20 D. 88
Correct Answer: B
Rationale: To calculate IQR = Q3 - Q1:
1. Order data: Already ordered: 12, 15, 18, 22, 25, 28, 32, 35, 100 (n=9)
2. Find median (Q2): The 5th value = 25
3. Find Q1 (median of lower half): Lower half = 12, 15, 18, 22. Q1 = (15 + 18)/2 = 16.5
4. Find Q3 (median of upper half): Upper half = 28, 32, 35, 100. Q3 = (32 + 35)/2 = 33.5
5. IQR = 33.5 - 16.5 = 17
• Option A (15) results from incorrectly using (22 - 18) or other incorrect quartile
calculations.
• Option C (20) might result from (35 - 15), confusing quartiles with raw data positions.
• Option D (88) is the full range (100 - 12), not the IQR.
The IQR represents the spread of the middle 50% of data, making it robust to outliers like the
value 100 in this dataset.
Q5: A box plot displays the following five-number summary for employee salaries (in
thousands): Min = $32K, Q1 = $45K, Median = $58K, Q3 = $72K, Max = $95K. Which statement
accurately interprets this distribution?
A. 50% of employees earn between $32K and $58K B. 75% of employees earn more than $72K
C. The middle 50% of salaries span $27K [CORRECT] D. The distribution is symmetric with no
skew
Correct Answer: C
Rationale: The IQR (middle 50%) = Q3 - Q1 = $72K - $45K = $27K. This correctly interprets the
box portion of the box plot.
, • Option A is incorrect—50% of employees earn below the median ($58K), not between
min and median. The lower 50% spans $32K to $58K ($26K range).
• Option B is reversed—75% of employees earn LESS than $72K (Q3 represents the 75th
percentile).
• Option D is incorrect—the distribution shows right skew: the upper whisker ($95K - $72K
= $23K) is longer than the lower whisker ($45K - $32K = $13K), and the median is closer
to Q1 than Q3.
Box plots efficiently display skewness and outliers, crucial for HR analytics and compensation
analysis.
Q6: A marketing team surveys 500 customers about brand preference (Brand A, B, or C). To
display the frequency distribution effectively, which graphical method is most appropriate?
A. Histogram B. Scatterplot C. Bar chart [CORRECT] D. Box plot
Correct Answer: C
Rationale: A bar chart is appropriate for displaying categorical data (nominal level: Brand A, B,
C). Bars are separated to emphasize distinct categories, and heights represent frequencies or
percentages.
• Option A (Histogram) is for continuous quantitative data where bars touch to show the
continuous scale.
• Option B (Scatterplot) displays the relationship between two quantitative variables.
• Option D (Box plot) summarizes distribution of a single quantitative variable.
In business reporting, choosing the correct graph prevents misinterpretation—using a histogram
for categorical data is a common error that implies false continuity between categories.
Q7: A dataset has a mean of 50 and a standard deviation of 10. Using the empirical rule,
approximately what percentage of data falls between 30 and 70?
A. 68% B. 95% [CORRECT] C. 99.7% D. 100%
Correct Answer: B
Rationale: The empirical rule (68-95-99.7 rule) for normal distributions states:
