MATH 225N STATISTICAL REASONING -
WEEK 2 COMPREHENSIVE QUESTIONS
AND VERIFIED ANSWERS |100%
CORRECT| GRADE A+
1. A dataset has a mean of 50 and a standard deviation of 5. According to the Empirical Rule,
what percentage of data falls between 40 and 60?
A. 68%
B. 99.7%
C. 95%
D. 75%
Answer: C
Conceptual Explanation: According to the Empirical Rule, approximately 95% of data in a
normal distribution falls within two standard deviations of the mean (50 ± 2*5 = 40 to 60).
2. Which measure of central tendency is most resistant to extreme outliers?
A. Mean
B. Range
C. Mode
D. Median
,Answer: D
Conceptual Explanation: The median is a resistant measure because it is based on the
middle position rather than the numerical values of every data point, unlike the mean.
3. In a right-skewed (positively skewed) distribution, which of the following is typically true?
A. Mean < Median < Mode
B. Mean = Median = Mode
C. Median < Mode < Mean
D. Mode < Median < Mean
Answer: D
Conceptual Explanation: In a right-skewed distribution, the tail extends to the right,
pulling the mean higher than the median and the mode.
4. A student scores 85 on a test where the mean is 75 and the standard deviation is 5. What is
the z-score?
A. 2.0
B. -2.0
C. 1.0
D. 0.5
Answer: A
, Conceptual Explanation: Z-score = (x - μ) / σ. Here, (85 - 75) / 5 = = 2.0.
5. If the variance of a sample is 16, what is the sample standard deviation?
A. 256
B. 8
C. 4
D. 2
Answer: C
Conceptual Explanation: The standard deviation is the square root of the variance. The
square root of 16 is 4.
6. Which of the following is required to calculate the Interquartile Range (IQR)?
A. Mean and Standard Deviation
B. Maximum and Minimum
C. Q3 and Q1
D. Mode and Median
Answer: C
Conceptual Explanation: The IQR is calculated by subtracting the first quartile (Q1) from
the third quartile (Q3).
WEEK 2 COMPREHENSIVE QUESTIONS
AND VERIFIED ANSWERS |100%
CORRECT| GRADE A+
1. A dataset has a mean of 50 and a standard deviation of 5. According to the Empirical Rule,
what percentage of data falls between 40 and 60?
A. 68%
B. 99.7%
C. 95%
D. 75%
Answer: C
Conceptual Explanation: According to the Empirical Rule, approximately 95% of data in a
normal distribution falls within two standard deviations of the mean (50 ± 2*5 = 40 to 60).
2. Which measure of central tendency is most resistant to extreme outliers?
A. Mean
B. Range
C. Mode
D. Median
,Answer: D
Conceptual Explanation: The median is a resistant measure because it is based on the
middle position rather than the numerical values of every data point, unlike the mean.
3. In a right-skewed (positively skewed) distribution, which of the following is typically true?
A. Mean < Median < Mode
B. Mean = Median = Mode
C. Median < Mode < Mean
D. Mode < Median < Mean
Answer: D
Conceptual Explanation: In a right-skewed distribution, the tail extends to the right,
pulling the mean higher than the median and the mode.
4. A student scores 85 on a test where the mean is 75 and the standard deviation is 5. What is
the z-score?
A. 2.0
B. -2.0
C. 1.0
D. 0.5
Answer: A
, Conceptual Explanation: Z-score = (x - μ) / σ. Here, (85 - 75) / 5 = = 2.0.
5. If the variance of a sample is 16, what is the sample standard deviation?
A. 256
B. 8
C. 4
D. 2
Answer: C
Conceptual Explanation: The standard deviation is the square root of the variance. The
square root of 16 is 4.
6. Which of the following is required to calculate the Interquartile Range (IQR)?
A. Mean and Standard Deviation
B. Maximum and Minimum
C. Q3 and Q1
D. Mode and Median
Answer: C
Conceptual Explanation: The IQR is calculated by subtracting the first quartile (Q1) from
the third quartile (Q3).
