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QMB 3200 Final Exam | University of Central Florida
(UCF) | Business Statistics – Descriptive Statistics,
Probability, Sampling, Inference, Hypothesis Testing,
Regression| Verified Answers
Exam Structure:
Subject: Business Statistics – Descriptive Statistics, Probability, Sampling, and
Inference (QMB 3200)
Source: QMB 3200 FINAL UCF – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. Suppose we have the following data: 12, 17, 13, 25, 16, 21, 30, 14,
16, and 18. To find the 10% trimmed mean, what numbers should be
deleted from the calculation?
Correct Answer: 12 and 30.
Rationale:
1. The 10% trimmed mean removes the smallest 10% and largest 10% of
observations.
2. With n=10, 10% of 10 = 1 observation from each end.
3. The smallest value is 12; the largest is 30.
4. Remove 12 and 30, then compute the mean of the remaining 8 values.
2. Which of the following is NOT resistant to outliers in a data set?
A. Median
B. Mean
C. Variance
D. Interquartile range
Correct Answer: B. Mean.
Rationale:
1. The mean is affected by extreme values because it uses all data points.
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2. The median is resistant (not affected by outliers).
3. Variance and standard deviation are also affected by outliers.
4. The interquartile range (IQR) is resistant because it focuses on the middle
50%.
3. The pth percentile is a value such that at least p percent of the
observations are:
Correct Answer: Less than or equal to this value.
Rationale:
1. The pth percentile divides the data so that at least p% fall at or below that
value.
2. Example: The 50th percentile (median) has 50% of observations ≤ that
value.
3. Percentiles are used to understand the relative standing of a data point.
4. Quartiles are specific percentiles (25th, 50th, 75th).
4. Which of the following provides a measure of central location for
the data?
A. Mean
B. Variance
C. Mode
D. Standard deviation
Correct Answer: A. Mean.
Rationale:
1. Measures of central location include mean, median, and mode.
2. Variance and standard deviation measure dispersion (spread).
3. The mean is the arithmetic average.
4. The mode is the most frequent value but is not always a measure of center.
5. When testing water for chemical impurities, results are often
reported as BDL (below detection limit). Data: 5, 7, 12, BDL, 10, 8, BDL,
20, 6. Which is correct?
A. The mean lead level is about 10 ppm.
B. The median lead level is 8 ppm.
C. The mean lead level is about 8 ppm.
D. The median lead level is 7 ppm.
Correct Answer: D. The median lead level is 7 ppm.
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Rationale:
1. Replace BDL with 0 (common practice for below detection limit).
2. Sorted data: 0, 0, 5, 6, 7, 8, 10, 12, 20.
3. Median (5th value) = 7 ppm.
4. Mean (0+0+5+6+7+8+10+12+20)/9 = 68/9 ≈ 7.56 ppm (not 8 or 10).
6. A student made scores of 85, 56, and 91 on her first three tests.
What score does she need on her next test to have an 80 test average?
Correct Answer: 88.
Rationale:
1. Average = (85 + 56 + 91 + x)/4 = 80.
2. 232 + x = 320.
3. x = 320 – 232 = 88.
4. She needs an 88 on the fourth test.
7. Growth factors for the population of Dallas in the past five years
have been 1, 2, 3, 4, and 5, respectively. The geometric mean is:
Correct Answer: Fifth root of 120 (∜120 or 120^(1/5)).
Rationale:
1. Geometric mean = (1 × 2 × 3 × 4 × 5)^(1/5).
2. Product = 120.
3. Geometric mean = 120^(1/5) ≈ 2.61.
4. Used for growth rates (multiplicative processes).
8. A sample of 99 distances has a mean of 24 feet and a median of 21.5
feet. An observation recorded as 30 actually had a value of 35. After
correction:
Correct Answer: The median remains the same, but the mean is increased.
Rationale:
1. Changing a value from 30 to 35 increases the sum of the data.
2. Mean = sum/n, so the mean increases.
3. The median (middle value) is unaffected by changing a single value (unless
that value is at the median position).
4. With n=99, the 50th value is the median; 30 and 35 are not necessarily
the median.
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9. A numerical value used as a summary measure for a sample, such as
sample mean, is known as a:
Correct Answer: Sample statistic.
Rationale:
1. A statistic describes a sample.
2. A parameter describes a population.
3. Examples: sample mean (x̄ ), sample standard deviation (s), sample
proportion (p̂ ).
4. Statistics are used to estimate population parameters.
10. The measure of location that is most likely to be influenced by
extreme values in a data set is the:
Correct Answer: Mean.
Rationale:
1. The mean uses all data points and is pulled toward extreme values.
2. The median is resistant to outliers.
3. The mode is not typically affected by extreme values.
4. Example: In data set {1,2,3,4,100}, mean = 22, median = 3.
11. A student found mean weight gain = 12.8 pounds, SD = 3.5 pounds.
The scale was out of calibration by 1.5 pounds (weighed items 1.5
pounds more). What are the corrected summary measures?
Correct Answer: The mean should be 11.3 and the standard deviation
should remain unchanged.
Rationale:
1. Subtracting a constant (1.5) from every observation reduces the mean by
that constant.
2. Corrected mean = 12.8 – 1.5 = 11.3.
3. Standard deviation is unchanged because subtracting a constant does not
affect spread.
4. Adding or subtracting a constant shifts all values equally, preserving
variability.
12. When a set of data has suspect outliers, which is the preferred
measure of central tendency?
Correct Answer: Median.
QMB 3200 Final Exam | University of Central Florida
(UCF) | Business Statistics – Descriptive Statistics,
Probability, Sampling, Inference, Hypothesis Testing,
Regression| Verified Answers
Exam Structure:
Subject: Business Statistics – Descriptive Statistics, Probability, Sampling, and
Inference (QMB 3200)
Source: QMB 3200 FINAL UCF – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. Suppose we have the following data: 12, 17, 13, 25, 16, 21, 30, 14,
16, and 18. To find the 10% trimmed mean, what numbers should be
deleted from the calculation?
Correct Answer: 12 and 30.
Rationale:
1. The 10% trimmed mean removes the smallest 10% and largest 10% of
observations.
2. With n=10, 10% of 10 = 1 observation from each end.
3. The smallest value is 12; the largest is 30.
4. Remove 12 and 30, then compute the mean of the remaining 8 values.
2. Which of the following is NOT resistant to outliers in a data set?
A. Median
B. Mean
C. Variance
D. Interquartile range
Correct Answer: B. Mean.
Rationale:
1. The mean is affected by extreme values because it uses all data points.
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2. The median is resistant (not affected by outliers).
3. Variance and standard deviation are also affected by outliers.
4. The interquartile range (IQR) is resistant because it focuses on the middle
50%.
3. The pth percentile is a value such that at least p percent of the
observations are:
Correct Answer: Less than or equal to this value.
Rationale:
1. The pth percentile divides the data so that at least p% fall at or below that
value.
2. Example: The 50th percentile (median) has 50% of observations ≤ that
value.
3. Percentiles are used to understand the relative standing of a data point.
4. Quartiles are specific percentiles (25th, 50th, 75th).
4. Which of the following provides a measure of central location for
the data?
A. Mean
B. Variance
C. Mode
D. Standard deviation
Correct Answer: A. Mean.
Rationale:
1. Measures of central location include mean, median, and mode.
2. Variance and standard deviation measure dispersion (spread).
3. The mean is the arithmetic average.
4. The mode is the most frequent value but is not always a measure of center.
5. When testing water for chemical impurities, results are often
reported as BDL (below detection limit). Data: 5, 7, 12, BDL, 10, 8, BDL,
20, 6. Which is correct?
A. The mean lead level is about 10 ppm.
B. The median lead level is 8 ppm.
C. The mean lead level is about 8 ppm.
D. The median lead level is 7 ppm.
Correct Answer: D. The median lead level is 7 ppm.
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Rationale:
1. Replace BDL with 0 (common practice for below detection limit).
2. Sorted data: 0, 0, 5, 6, 7, 8, 10, 12, 20.
3. Median (5th value) = 7 ppm.
4. Mean (0+0+5+6+7+8+10+12+20)/9 = 68/9 ≈ 7.56 ppm (not 8 or 10).
6. A student made scores of 85, 56, and 91 on her first three tests.
What score does she need on her next test to have an 80 test average?
Correct Answer: 88.
Rationale:
1. Average = (85 + 56 + 91 + x)/4 = 80.
2. 232 + x = 320.
3. x = 320 – 232 = 88.
4. She needs an 88 on the fourth test.
7. Growth factors for the population of Dallas in the past five years
have been 1, 2, 3, 4, and 5, respectively. The geometric mean is:
Correct Answer: Fifth root of 120 (∜120 or 120^(1/5)).
Rationale:
1. Geometric mean = (1 × 2 × 3 × 4 × 5)^(1/5).
2. Product = 120.
3. Geometric mean = 120^(1/5) ≈ 2.61.
4. Used for growth rates (multiplicative processes).
8. A sample of 99 distances has a mean of 24 feet and a median of 21.5
feet. An observation recorded as 30 actually had a value of 35. After
correction:
Correct Answer: The median remains the same, but the mean is increased.
Rationale:
1. Changing a value from 30 to 35 increases the sum of the data.
2. Mean = sum/n, so the mean increases.
3. The median (middle value) is unaffected by changing a single value (unless
that value is at the median position).
4. With n=99, the 50th value is the median; 30 and 35 are not necessarily
the median.
, 4|Page
9. A numerical value used as a summary measure for a sample, such as
sample mean, is known as a:
Correct Answer: Sample statistic.
Rationale:
1. A statistic describes a sample.
2. A parameter describes a population.
3. Examples: sample mean (x̄ ), sample standard deviation (s), sample
proportion (p̂ ).
4. Statistics are used to estimate population parameters.
10. The measure of location that is most likely to be influenced by
extreme values in a data set is the:
Correct Answer: Mean.
Rationale:
1. The mean uses all data points and is pulled toward extreme values.
2. The median is resistant to outliers.
3. The mode is not typically affected by extreme values.
4. Example: In data set {1,2,3,4,100}, mean = 22, median = 3.
11. A student found mean weight gain = 12.8 pounds, SD = 3.5 pounds.
The scale was out of calibration by 1.5 pounds (weighed items 1.5
pounds more). What are the corrected summary measures?
Correct Answer: The mean should be 11.3 and the standard deviation
should remain unchanged.
Rationale:
1. Subtracting a constant (1.5) from every observation reduces the mean by
that constant.
2. Corrected mean = 12.8 – 1.5 = 11.3.
3. Standard deviation is unchanged because subtracting a constant does not
affect spread.
4. Adding or subtracting a constant shifts all values equally, preserving
variability.
12. When a set of data has suspect outliers, which is the preferred
measure of central tendency?
Correct Answer: Median.
