STAT 200 ADVANCED STATISTICS
COMPREHENSIVE EXAM (2026/2027)
QUESTIONS AND ANSWERS
1. Which level of measurement allows for the classification of data into categories with a
natural order, but lacks a consistent measurable difference between categories?
A. Ordinal
B. Nominal
C. Interval
D. Ratio
Answer: A
Conceptual Explanation: Ordinal data can be ranked or ordered, but the mathematical
difference between ranks (e.g., ‘satisfied’ vs ‘very satisfied’) is not uniform or quantifiable.
2. A researcher finds that a dataset’s mean is 50 and the median is 40. Which of the following
is most likely true about the distribution?
A. The distribution is symmetric.
,B. The distribution is negatively skewed.
C. The distribution is positively skewed.
D. The distribution is bimodal.
Answer: C
Conceptual Explanation: In a positively skewed (right-skewed) distribution, the mean is
typically greater than the median because the outliers in the tail pull the mean toward
them.
3. If every value in a dataset is multiplied by a constant factor of 3, how does the variance of
the new dataset compare to the original variance?
A. The variance is 3 times larger.
B. The variance is 6 times larger.
C. The variance is 9 times larger.
D. The variance remains unchanged.
Answer: C
Conceptual Explanation: Variance is the square of the standard deviation. When values
are scaled by ‘k’, the standard deviation increases by ‘k’ and the variance increases by ‘k
squared’. 3 squared is 9.
, 4. Which of the following sampling methods involves dividing the population into groups and
then selecting all individuals from a few randomly selected groups?
A. Stratified Sampling
B. Systematic Sampling
C. Simple Random Sampling
D. Cluster Sampling
Answer: D
Conceptual Explanation: Cluster sampling involves dividing the population into clusters,
randomly selecting clusters, and surveying every member within those chosen clusters.
5. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The population is normal, regardless of sample size.
B. The sample size is large (typically n > 30).
C. The population variance is known.
D. Both A and B are correct.
Answer: D
Conceptual Explanation: The CLT states the sampling distribution becomes normal as n
increases (n>30 rule of thumb) or if the underlying population was already normal.
COMPREHENSIVE EXAM (2026/2027)
QUESTIONS AND ANSWERS
1. Which level of measurement allows for the classification of data into categories with a
natural order, but lacks a consistent measurable difference between categories?
A. Ordinal
B. Nominal
C. Interval
D. Ratio
Answer: A
Conceptual Explanation: Ordinal data can be ranked or ordered, but the mathematical
difference between ranks (e.g., ‘satisfied’ vs ‘very satisfied’) is not uniform or quantifiable.
2. A researcher finds that a dataset’s mean is 50 and the median is 40. Which of the following
is most likely true about the distribution?
A. The distribution is symmetric.
,B. The distribution is negatively skewed.
C. The distribution is positively skewed.
D. The distribution is bimodal.
Answer: C
Conceptual Explanation: In a positively skewed (right-skewed) distribution, the mean is
typically greater than the median because the outliers in the tail pull the mean toward
them.
3. If every value in a dataset is multiplied by a constant factor of 3, how does the variance of
the new dataset compare to the original variance?
A. The variance is 3 times larger.
B. The variance is 6 times larger.
C. The variance is 9 times larger.
D. The variance remains unchanged.
Answer: C
Conceptual Explanation: Variance is the square of the standard deviation. When values
are scaled by ‘k’, the standard deviation increases by ‘k’ and the variance increases by ‘k
squared’. 3 squared is 9.
, 4. Which of the following sampling methods involves dividing the population into groups and
then selecting all individuals from a few randomly selected groups?
A. Stratified Sampling
B. Systematic Sampling
C. Simple Random Sampling
D. Cluster Sampling
Answer: D
Conceptual Explanation: Cluster sampling involves dividing the population into clusters,
randomly selecting clusters, and surveying every member within those chosen clusters.
5. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The population is normal, regardless of sample size.
B. The sample size is large (typically n > 30).
C. The population variance is known.
D. Both A and B are correct.
Answer: D
Conceptual Explanation: The CLT states the sampling distribution becomes normal as n
increases (n>30 rule of thumb) or if the underlying population was already normal.
