MATH 110 MODULE 2 - DESCRIPTIVE
STATISTICS COMPREHENSIVE EXAM
2026/2027 UPDATE. JUST RELEASED
1. Which of the following measures of central tendency is the most sensitive to extreme
values or outliers in a dataset?
A. Median
B. Geometric Mean
C. Mode
D. Arithmetic Mean
Answer: D
Conceptual Explanation: The arithmetic mean involves every value in the calculation, so
an outlier significantly pulls the mean toward it. The median and mode are resistant
measures.
2. A researcher calculates a coefficient of variation (CV) for two groups. Group A has a CV of
15% and Group B has a CV of 25%. Which statement is true?
A. Group A has higher relative variability.
B. Group B has higher relative variability.
C. Group A has a higher standard deviation than Group B.
,D. Both groups have equal absolute variability.
Answer: B
Conceptual Explanation: Coefficient of variation measures relative variability; a higher
percentage indicates more variability relative to the mean.
3. In a symmetric distribution, what is the relationship between the mean, median, and
mode?
A. Mean > Median > Mode
B. Mean < Median < Mode
C. Mean = Median = Mode
D. Mean = Median, but Mode is different
Answer: C
Conceptual Explanation: In a perfectly symmetric unimodal distribution, the mean,
median, and mode are all located at the center.
4. Which theorem states that at least 75% of the data in any distribution must lie within two
standard deviations of the mean?
A. Empirical Rule
B. Chebyshev’s Theorem
C. Central Limit Theorem
D. Law of Large Numbers
, Answer: B
Conceptual Explanation: Chebyshev’s Theorem applies to any distribution shape and
states that at least (1 - 1/k^2) of data falls within k standard deviations. For k=2, it is 1 -
1/4 = 0.75.
5. According to the Empirical Rule, approximately what percentage of data falls between -3
and +3 standard deviations from the mean in a bell-shaped distribution?
A. 68%
B. 95%
C. 100%
D. 99.7%
Answer: D
Conceptual Explanation: The Empirical Rule (68-95-99.7) states that 99.7% of data in a
normal distribution falls within 3 standard deviations.
6. When calculating the sample variance, why is the denominator n-1 instead of n?
A. To make the variance larger
B. To ensure the standard deviation is positive
C. To account for the mean being a constant
D. To correct for bias in the estimation of the population variance
Answer: D
STATISTICS COMPREHENSIVE EXAM
2026/2027 UPDATE. JUST RELEASED
1. Which of the following measures of central tendency is the most sensitive to extreme
values or outliers in a dataset?
A. Median
B. Geometric Mean
C. Mode
D. Arithmetic Mean
Answer: D
Conceptual Explanation: The arithmetic mean involves every value in the calculation, so
an outlier significantly pulls the mean toward it. The median and mode are resistant
measures.
2. A researcher calculates a coefficient of variation (CV) for two groups. Group A has a CV of
15% and Group B has a CV of 25%. Which statement is true?
A. Group A has higher relative variability.
B. Group B has higher relative variability.
C. Group A has a higher standard deviation than Group B.
,D. Both groups have equal absolute variability.
Answer: B
Conceptual Explanation: Coefficient of variation measures relative variability; a higher
percentage indicates more variability relative to the mean.
3. In a symmetric distribution, what is the relationship between the mean, median, and
mode?
A. Mean > Median > Mode
B. Mean < Median < Mode
C. Mean = Median = Mode
D. Mean = Median, but Mode is different
Answer: C
Conceptual Explanation: In a perfectly symmetric unimodal distribution, the mean,
median, and mode are all located at the center.
4. Which theorem states that at least 75% of the data in any distribution must lie within two
standard deviations of the mean?
A. Empirical Rule
B. Chebyshev’s Theorem
C. Central Limit Theorem
D. Law of Large Numbers
, Answer: B
Conceptual Explanation: Chebyshev’s Theorem applies to any distribution shape and
states that at least (1 - 1/k^2) of data falls within k standard deviations. For k=2, it is 1 -
1/4 = 0.75.
5. According to the Empirical Rule, approximately what percentage of data falls between -3
and +3 standard deviations from the mean in a bell-shaped distribution?
A. 68%
B. 95%
C. 100%
D. 99.7%
Answer: D
Conceptual Explanation: The Empirical Rule (68-95-99.7) states that 99.7% of data in a
normal distribution falls within 3 standard deviations.
6. When calculating the sample variance, why is the denominator n-1 instead of n?
A. To make the variance larger
B. To ensure the standard deviation is positive
C. To account for the mean being a constant
D. To correct for bias in the estimation of the population variance
Answer: D
