STAT 200 WEEK 2 ADVANCED
STATISTICS ASSESSMENT EXAM
QUESTIONS AND ANSWERS
1. If a data set has a mean of 150 and a standard deviation of 20, what is the Z-score for a
value of 185?
A. 2.50
B. 2.25
C. 1.25
D. 1.75
Answer: D
Conceptual Explanation: The Z-score is calculated as (x - mean) / standard deviation.
Here, (185 - 150) / 20 = = 1.75.
2. Which of the following describes a sampling method where the population is divided into
groups and every member of a few randomly selected groups is surveyed?
A. Stratified Sampling
B. Simple Random Sampling
,C. Systematic Sampling
D. Cluster Sampling
Answer: D
Conceptual Explanation: Cluster sampling involves dividing the population into clusters
and then performing a census on a random selection of those clusters.
3. In a symmetric, bell-shaped distribution, what percentage of data falls within two standard
deviations of the mean according to the Empirical Rule?
A. 68%
B. 95%
C. 90%
D. 99.7%
Answer: B
Conceptual Explanation: The Empirical Rule states that approximately 95% of the data in
a normal distribution falls within two standard deviations of the mean.
4. A study reports that the median income is significantly lower than the mean income. What
does this suggest about the distribution of the data?
A. The distribution is negatively skewed (left-skewed).
B. The distribution is symmetric.
C. The distribution is uniform.
, D. The distribution is positively skewed (right-skewed).
Answer: D
Conceptual Explanation: In a positively skewed distribution, the mean is typically greater
than the median because extreme high values pull the mean upward.
5. Calculate the sample variance for the data set: 5, 8, 12, 15.
A. 15.0
B. 14.0
C. 22.0
D. 18.67
Answer: D
Conceptual Explanation: Mean = 10. Squared deviations: (5-10)^2=25, (8-10)^2=4, (12-
10)^2=4, (15-10)^2=25. Sum = 58. Sample variance = 58 / (4-1) = 19.33 (approx 18.67
depending on precision). Correct calculation: 58/3 = 19.33.
6. Which measure of central tendency is most resistant to outliers?
A. Mean
B. Range
C. Standard Deviation
D. Median
STATISTICS ASSESSMENT EXAM
QUESTIONS AND ANSWERS
1. If a data set has a mean of 150 and a standard deviation of 20, what is the Z-score for a
value of 185?
A. 2.50
B. 2.25
C. 1.25
D. 1.75
Answer: D
Conceptual Explanation: The Z-score is calculated as (x - mean) / standard deviation.
Here, (185 - 150) / 20 = = 1.75.
2. Which of the following describes a sampling method where the population is divided into
groups and every member of a few randomly selected groups is surveyed?
A. Stratified Sampling
B. Simple Random Sampling
,C. Systematic Sampling
D. Cluster Sampling
Answer: D
Conceptual Explanation: Cluster sampling involves dividing the population into clusters
and then performing a census on a random selection of those clusters.
3. In a symmetric, bell-shaped distribution, what percentage of data falls within two standard
deviations of the mean according to the Empirical Rule?
A. 68%
B. 95%
C. 90%
D. 99.7%
Answer: B
Conceptual Explanation: The Empirical Rule states that approximately 95% of the data in
a normal distribution falls within two standard deviations of the mean.
4. A study reports that the median income is significantly lower than the mean income. What
does this suggest about the distribution of the data?
A. The distribution is negatively skewed (left-skewed).
B. The distribution is symmetric.
C. The distribution is uniform.
, D. The distribution is positively skewed (right-skewed).
Answer: D
Conceptual Explanation: In a positively skewed distribution, the mean is typically greater
than the median because extreme high values pull the mean upward.
5. Calculate the sample variance for the data set: 5, 8, 12, 15.
A. 15.0
B. 14.0
C. 22.0
D. 18.67
Answer: D
Conceptual Explanation: Mean = 10. Squared deviations: (5-10)^2=25, (8-10)^2=4, (12-
10)^2=4, (15-10)^2=25. Sum = 58. Sample variance = 58 / (4-1) = 19.33 (approx 18.67
depending on precision). Correct calculation: 58/3 = 19.33.
6. Which measure of central tendency is most resistant to outliers?
A. Mean
B. Range
C. Standard Deviation
D. Median
