STATISTICS FOR THE SCIENCES
MATH 3339 Exam 1-2 2026/2027
A+
Complete Blueprint Coverage · Probability & Statistical Inference
A+ 4 100%
QUESTIONS VERIFIED EXAM DOMAINS COVERED RATIONALES INCLUDED
CATEGORIES
Descriptive Statistics and Graphical Methods
Probability, Counting, and Conditional Probability
Random Variables and Probability Distributions
Sampling Distributions, Estimation, and Hypothesis Testing
STUVIAACTUALEXAM
,SECTION 1: DESCRIPTIVE STATISTICS AND GRAPHICAL METHODS
Q1.
A data set of 20 exam scores has a mean of 78 and a median of 82. The distribution is most likely:
A. Symmetric about the mean
B. Left-skewed (negatively skewed), because the mean is pulled toward the lower tail
C. Right-skewed, because the median is higher than the mean
D. Uniform with no skew
Correct Answer: C
Rationale:
When the mean is less than the median, the left tail tends to be longer, pulling the mean downward. This is the classic pattern of left
(negative) skew.
Q2.
A researcher constructs a boxplot and observes that the right whisker is much longer than the left whisker and there are
several points beyond the upper fence. What does this indicate?
A. The data are left-skewed with low outliers
B. The data are right-skewed and contain high outliers
C. The data are perfectly symmetric
D. The interquartile range is zero
Correct Answer: D
Rationale:
A longer upper whisker and points beyond the upper fence indicate a right-skewed distribution with high outliers.
Q3.
For the data set {4, 7, 7, 8, 10, 12, 15}, what is the sample interquartile range (IQR)?
A. 3
B. 5
C. 7
D. 11
Correct Answer: C
Rationale:
Ordered data: Q1 is the median of {4,7,7} = 7; Q3 is the median of {10,12,15} = 12. IQR = 12 − 7 = 5.
, Q4.
A histogram of a large sample shows a roughly bell-shaped, symmetric distribution. Which measure of center is most
appropriate and robust for summarizing the typical value?
A. The mode only
B. The mean (and the median will be similar)
C. The range
D. The maximum value
Correct Answer: B
Rationale:
For approximately symmetric, unimodal data the mean is an efficient measure of center; the median will be close to the mean.
Q5.
The standard deviation of a sample is 0. What does this imply about the data values?
A. The data contain both positive and negative numbers that cancel
B. All observations are identical (there is no variability)
C. The mean must be zero
D. The sample size is 1 only
Correct Answer: C
Rationale:
Standard deviation is zero if and only if every observation equals the mean, i.e., all values are the same.
Q6.
A z-score for an observation is −2.3. Relative to the sample mean and standard deviation, this observation is:
A. 2.3 standard deviations above the mean
B. 2.3 standard deviations below the mean
C. At the mean
D. Impossible because z-scores cannot be negative
Correct Answer: D
Rationale:
A negative z-score indicates the value lies below the mean; the magnitude gives the number of standard deviations.
Q7.
In a sample of size 40, the 25th percentile is 62 and the 75th percentile is 88. An observation of 130 is examined using
the 1.5×IQR rule. Is it an outlier?
A. No, because 130 is less than Q3
B. Yes; the upper fence is Q3 + 1.5×IQR = 88 + 1.5×26 = 127, and 130 exceeds it
C. No, because only values below Q1 can be outliers
D. The rule cannot be applied without the mean
Correct Answer: A
Rationale:
IQR = 26; upper fence = 88 + 39 = 127. Since 130 > 127, the observation is flagged as a potential outlier.
MATH 3339 Exam 1-2 2026/2027
A+
Complete Blueprint Coverage · Probability & Statistical Inference
A+ 4 100%
QUESTIONS VERIFIED EXAM DOMAINS COVERED RATIONALES INCLUDED
CATEGORIES
Descriptive Statistics and Graphical Methods
Probability, Counting, and Conditional Probability
Random Variables and Probability Distributions
Sampling Distributions, Estimation, and Hypothesis Testing
STUVIAACTUALEXAM
,SECTION 1: DESCRIPTIVE STATISTICS AND GRAPHICAL METHODS
Q1.
A data set of 20 exam scores has a mean of 78 and a median of 82. The distribution is most likely:
A. Symmetric about the mean
B. Left-skewed (negatively skewed), because the mean is pulled toward the lower tail
C. Right-skewed, because the median is higher than the mean
D. Uniform with no skew
Correct Answer: C
Rationale:
When the mean is less than the median, the left tail tends to be longer, pulling the mean downward. This is the classic pattern of left
(negative) skew.
Q2.
A researcher constructs a boxplot and observes that the right whisker is much longer than the left whisker and there are
several points beyond the upper fence. What does this indicate?
A. The data are left-skewed with low outliers
B. The data are right-skewed and contain high outliers
C. The data are perfectly symmetric
D. The interquartile range is zero
Correct Answer: D
Rationale:
A longer upper whisker and points beyond the upper fence indicate a right-skewed distribution with high outliers.
Q3.
For the data set {4, 7, 7, 8, 10, 12, 15}, what is the sample interquartile range (IQR)?
A. 3
B. 5
C. 7
D. 11
Correct Answer: C
Rationale:
Ordered data: Q1 is the median of {4,7,7} = 7; Q3 is the median of {10,12,15} = 12. IQR = 12 − 7 = 5.
, Q4.
A histogram of a large sample shows a roughly bell-shaped, symmetric distribution. Which measure of center is most
appropriate and robust for summarizing the typical value?
A. The mode only
B. The mean (and the median will be similar)
C. The range
D. The maximum value
Correct Answer: B
Rationale:
For approximately symmetric, unimodal data the mean is an efficient measure of center; the median will be close to the mean.
Q5.
The standard deviation of a sample is 0. What does this imply about the data values?
A. The data contain both positive and negative numbers that cancel
B. All observations are identical (there is no variability)
C. The mean must be zero
D. The sample size is 1 only
Correct Answer: C
Rationale:
Standard deviation is zero if and only if every observation equals the mean, i.e., all values are the same.
Q6.
A z-score for an observation is −2.3. Relative to the sample mean and standard deviation, this observation is:
A. 2.3 standard deviations above the mean
B. 2.3 standard deviations below the mean
C. At the mean
D. Impossible because z-scores cannot be negative
Correct Answer: D
Rationale:
A negative z-score indicates the value lies below the mean; the magnitude gives the number of standard deviations.
Q7.
In a sample of size 40, the 25th percentile is 62 and the 75th percentile is 88. An observation of 130 is examined using
the 1.5×IQR rule. Is it an outlier?
A. No, because 130 is less than Q3
B. Yes; the upper fence is Q3 + 1.5×IQR = 88 + 1.5×26 = 127, and 130 exceeds it
C. No, because only values below Q1 can be outliers
D. The rule cannot be applied without the mean
Correct Answer: A
Rationale:
IQR = 26; upper fence = 88 + 39 = 127. Since 130 > 127, the observation is flagged as a potential outlier.
