MATH 110 Statistics Final Exam – Portage
Learning Latest 2026/2027 Edition: Actual Exam
Questions with Verified Answers – Complete
Study Guide – Graded A+
SECTION 1: DESCRIPTIVE STATISTICS (Questions 1-10)
Q1: A researcher records the political party affiliation (Democrat, Republican,
Independent, Other) of survey respondents. This variable is measured at which level of
measurement?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Correct Answer: A
Rationale: Political party affiliation is categorical with no inherent order or ranking,
making it nominal. Ordinal (B) requires meaningful order (e.g., education levels); interval
(C) requires equal intervals but no true zero (e.g., temperature in Celsius); ratio (D)
requires equal intervals and a true zero (e.g., height, weight). The key distinction is that
nominal categories cannot be ranked—there's no "higher" or "lower" political party.
(Topic: Data Classification | Difficulty: Easy)
,Q2: Which of the following is a discrete variable?
A. The weight of a package in pounds
B. The number of students in a classroom
C. The temperature outside in degrees Fahrenheit
D. The time it takes to complete a marathon
Correct Answer: B
Rationale: Discrete variables take countable, finite values (typically whole numbers). The
number of students is countable (you cannot have 23.7 students). Continuous variables
(A, C, D) can take any value in a range and are measured, not counted. Weight,
temperature, and time can all have fractional values, making them continuous. This
distinction is crucial for selecting appropriate probability distributions.
(Topic: Data Classification | Difficulty: Easy)
Q3: A dataset has a mean of 45, median of 42, and mode of 38. What is the most likely
shape of this distribution?
A. Symmetric
B. Uniform
C. Right-skewed (positively skewed)
D. Left-skewed (negatively skewed)
Correct Answer: C
,Rationale: In a right-skewed distribution, the tail extends toward higher values, pulling
the mean upward while the median stays more central and the mode remains at the
peak. The pattern mean > median > mode (45 > 42 > 38) indicates right skew. Left skew
would show mode > median > mean; symmetric distributions have mean ≈ median ≈
mode. This relationship helps identify outliers and appropriate measures of center.
(Topic: Measures of Central Tendency | Difficulty: Medium)
Q4: Calculate the sample standard deviation for the dataset: 5, 8, 11, 14, 17.
A. 4.00
B. 4.24
C. 4.47
D. 5.00
Correct Answer: C
Rationale: Step 1: Find mean x̄ = (5+8+11+14+17)/5 = 55/5 = 11. Step 2: Calculate
squared deviations: (5-11)²=36, (8-11)²=9, (11-11)²=0, (14-11)²=9, (17-11)²=36. Sum =
90. Step 3: Divide by n-1 (sample): 90/4 = 22.5. Step 4: Square root: √22.5 = 4.47. Using
n instead of n-1 gives 4.24 (B); using wrong mean calculations gives other distractors.
Always use n-1 for sample standard deviation.
(Topic: Measures of Dispersion | Difficulty: Medium | Formula: s = √[Σ(x-x̄)²/(n-1)])
Q5: For a normal distribution with mean μ = 100 and standard deviation σ = 15, what
percentage of data falls between 70 and 130 according to the empirical rule?
A. 68%
, B. 95%
C. 99.7%
D. 100%
Correct Answer: B
Rationale: The empirical rule (68-95-99.7 rule) states that for normal distributions: ≈68%
within 1σ, ≈95% within 2σ, ≈99.7% within 3σ. Here, 70 = 100 - 2(15) and 130 = 100 +
2(15), so this is ±2σ, containing approximately 95% of data. This rule applies only to
normal distributions; Chebyshev's theorem applies to any distribution but gives wider
intervals (e.g., at least 75% within 2 standard deviations).
(Topic: Empirical Rule | Difficulty: Easy)
Q6: A student's exam score is at the 85th percentile. This means:
A. The student answered 85% of questions correctly
B. The student scored higher than 85% of all test-takers
C. 85% of students scored higher than this student
D. The student's z-score is 0.85
Correct Answer: B
Rationale: The 85th percentile indicates the student scored equal to or higher than 85%
of the reference group. Percentiles measure relative standing, not raw percentage
correct (A). Option C describes the 15th percentile; z-score 0.85 (D) corresponds to
approximately the 80th percentile, not 85th. Percentiles are useful for comparing scores
across different scales or distributions.
Learning Latest 2026/2027 Edition: Actual Exam
Questions with Verified Answers – Complete
Study Guide – Graded A+
SECTION 1: DESCRIPTIVE STATISTICS (Questions 1-10)
Q1: A researcher records the political party affiliation (Democrat, Republican,
Independent, Other) of survey respondents. This variable is measured at which level of
measurement?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Correct Answer: A
Rationale: Political party affiliation is categorical with no inherent order or ranking,
making it nominal. Ordinal (B) requires meaningful order (e.g., education levels); interval
(C) requires equal intervals but no true zero (e.g., temperature in Celsius); ratio (D)
requires equal intervals and a true zero (e.g., height, weight). The key distinction is that
nominal categories cannot be ranked—there's no "higher" or "lower" political party.
(Topic: Data Classification | Difficulty: Easy)
,Q2: Which of the following is a discrete variable?
A. The weight of a package in pounds
B. The number of students in a classroom
C. The temperature outside in degrees Fahrenheit
D. The time it takes to complete a marathon
Correct Answer: B
Rationale: Discrete variables take countable, finite values (typically whole numbers). The
number of students is countable (you cannot have 23.7 students). Continuous variables
(A, C, D) can take any value in a range and are measured, not counted. Weight,
temperature, and time can all have fractional values, making them continuous. This
distinction is crucial for selecting appropriate probability distributions.
(Topic: Data Classification | Difficulty: Easy)
Q3: A dataset has a mean of 45, median of 42, and mode of 38. What is the most likely
shape of this distribution?
A. Symmetric
B. Uniform
C. Right-skewed (positively skewed)
D. Left-skewed (negatively skewed)
Correct Answer: C
,Rationale: In a right-skewed distribution, the tail extends toward higher values, pulling
the mean upward while the median stays more central and the mode remains at the
peak. The pattern mean > median > mode (45 > 42 > 38) indicates right skew. Left skew
would show mode > median > mean; symmetric distributions have mean ≈ median ≈
mode. This relationship helps identify outliers and appropriate measures of center.
(Topic: Measures of Central Tendency | Difficulty: Medium)
Q4: Calculate the sample standard deviation for the dataset: 5, 8, 11, 14, 17.
A. 4.00
B. 4.24
C. 4.47
D. 5.00
Correct Answer: C
Rationale: Step 1: Find mean x̄ = (5+8+11+14+17)/5 = 55/5 = 11. Step 2: Calculate
squared deviations: (5-11)²=36, (8-11)²=9, (11-11)²=0, (14-11)²=9, (17-11)²=36. Sum =
90. Step 3: Divide by n-1 (sample): 90/4 = 22.5. Step 4: Square root: √22.5 = 4.47. Using
n instead of n-1 gives 4.24 (B); using wrong mean calculations gives other distractors.
Always use n-1 for sample standard deviation.
(Topic: Measures of Dispersion | Difficulty: Medium | Formula: s = √[Σ(x-x̄)²/(n-1)])
Q5: For a normal distribution with mean μ = 100 and standard deviation σ = 15, what
percentage of data falls between 70 and 130 according to the empirical rule?
A. 68%
, B. 95%
C. 99.7%
D. 100%
Correct Answer: B
Rationale: The empirical rule (68-95-99.7 rule) states that for normal distributions: ≈68%
within 1σ, ≈95% within 2σ, ≈99.7% within 3σ. Here, 70 = 100 - 2(15) and 130 = 100 +
2(15), so this is ±2σ, containing approximately 95% of data. This rule applies only to
normal distributions; Chebyshev's theorem applies to any distribution but gives wider
intervals (e.g., at least 75% within 2 standard deviations).
(Topic: Empirical Rule | Difficulty: Easy)
Q6: A student's exam score is at the 85th percentile. This means:
A. The student answered 85% of questions correctly
B. The student scored higher than 85% of all test-takers
C. 85% of students scored higher than this student
D. The student's z-score is 0.85
Correct Answer: B
Rationale: The 85th percentile indicates the student scored equal to or higher than 85%
of the reference group. Percentiles measure relative standing, not raw percentage
correct (A). Option C describes the 15th percentile; z-score 0.85 (D) corresponds to
approximately the 80th percentile, not 85th. Percentiles are useful for comparing scores
across different scales or distributions.
