STATISTICS BEC1 — Pre-Assessment 2026/2027 60 Questions · Multiple Choice
STATISTICS BEC1 STATISTICS PRE
ASSESSMENT 2026/2027
Comprehensive Pre-Assessment Examination — Introductory Statistics
Aligned with BEC1 Statistics Course Syllabus & College-Level Statistics Standards (2026/2027 Edition)
Total Questions: 60 · Sections: 6 · Format: Multiple Choice (4 options, one correct) · Cognitive Mix: 20% Recall,
50% Application, 30% Analysis
Section 1: Descriptive Statistics
Q1: A student recorded the number of hours five classmates spent studying last week: 4, 6,
8, 10, and 12. What is the sample mean of these study hours?
A. 7.0 hours
B. 8.0 hours *[CORRECT]*
C. 9.0 hours
D. 10.0 hours
Correct Answer: B
Rationale: Sum = 4+6+8+10+12 = 40; mean = 40 ÷ 5 = 8.0 hours. Option A divides by the wrong n+1, C and D
reflect miscounted sums. The arithmetic mean of an ungrouped dataset is the sum of observations divided by the
count, a foundational BEC1 descriptive-statistics competency.
Q2: Seven patients reported their systolic blood pressure (mmHg): 118, 122, 124, 125, 127,
130, 145. What is the median blood pressure?
A. 122 mmHg
B. 124 mmHg
C. 125 mmHg *[CORRECT]*
D. 127 mmHg
Correct Answer: C
Rationale: With n = 7 (odd), the median is the middle ordered value, the 4th observation = 125 mmHg. Option A is
Q1, D is close to Q3. The median is resistant to the high outlier (145), illustrating why it is preferred over the mean
for skewed clinical data.
BEC1 Statistics Pre-Assessment Page 1
,STATISTICS BEC1 — Pre-Assessment 2026/2027 60 Questions · Multiple Choice
Q3: A grocery manager counted the daily number of customers buying avocados for a
week: 12, 15, 12, 18, 12, 20, 15. Which of the following correctly describes the mode(s) of
this dataset?
A. 12 only
B. 15 only
C. Both 12 and 15 (bimodal) *[CORRECT]*
D. No mode exists
Correct Answer: C
Rationale: Both 12 and 15 each appear three times — more frequently than any other value — so the dataset is
bimodal. Option A and B each capture only one mode, while D is wrong because at least one value repeats.
Identifying multimodality signals whether a single typical value adequately summarizes the distribution.
Q4: An instructor tells a class: “The range of scores on the midterm was 45 points.” Which
statement is statistically correct?
A. The standard deviation is approximately 45 points.
B. The mean score must have been 45 points.
C. The difference between the highest and lowest score was 45 points. *[CORRECT]*
D. Most students scored within 45 points of the mean.
Correct Answer: C
Rationale: The range is defined as max − min, so a range of 45 means the gap between the highest and lowest
observed scores is 45. Range tells us nothing directly about standard deviation (A), the mean (B), or the spread
around the mean (D). It is the simplest but least stable measure of dispersion.
Q5: A sample of five weekly sales (in units) is: 10, 10, 10, 10, 10. What is the sample
variance?
A. 0 (because every value equals the mean) *[CORRECT]*
B. 1 (the count of distinct values)
C. 10 (the mean itself)
D. Undefined because the data are constant
Correct Answer: A
Rationale: When every observation equals the mean, every deviation is zero, so the sum of squared deviations and
therefore the sample variance s² are both zero. The variance is well-defined and equals zero — there is no spread.
Option D confuses zero variance with division-by-zero; the divisor n − 1 = 4 ≠ 0.
Q6: A dataset has a variance of 49. What is its standard deviation?
A. 7 *[CORRECT]*
B. 24.5
C. 49
D. 2401
Correct Answer: A
Rationale: The standard deviation is the square root of the variance, so √49 = 7. Option B is half of 49, C confuses
standard deviation with variance itself, and D squares 49. Standard deviation returns the measure to the original
units, which is why it is the dispersion measure most often reported in BEC1 coursework.
BEC1 Statistics Pre-Assessment Page 2
, STATISTICS BEC1 — Pre-Assessment 2026/2027 60 Questions · Multiple Choice
Q7: Two production lines report the following: Line A mean = 500 g, standard deviation = 10
g; Line B mean = 1000 g, standard deviation = 15 g. Which line has the greater relative
variability as measured by the coefficient of variation (CV)?
A. Line A (CV = 2.0%) *[CORRECT]*
B. Line B (CV = 1.5%)
C. Both lines have identical CV
D. Cannot be compared because means differ
Correct Answer: A
Rationale: CV = (s / mean) × 100%. Line A: (10/500) × 100% = 2.0%. Line B: (15/1000) × 100% = 1.5%. Despite
Line B having a larger absolute standard deviation, Line A has greater relative variability. CV is the appropriate
tool for comparing dispersion across datasets with different units or magnitudes.
Q8: On a standardized statistics exam scored out of 100, a student's score of 78
corresponds to the 70th percentile. Which interpretation is correct?
A. The student answered 78% of the questions correctly.
B. The student scored higher than 78% of test takers.
C. The student scored higher than 70% of test takers. *[CORRECT]*
D. 70% of the questions were answered correctly.
Correct Answer: C
Rationale: A percentile rank of 70 means the student's score exceeds approximately 70% of all scores in the
reference group. Option A confuses the raw score with a percentage of items correct, B inverts percentile and
score, and D confuses percentile with item-level performance. Percentiles measure relative position, not absolute
correctness.
Q9: For a dataset, Q1 = 20 and Q3 = 50. What are the interquartile range (IQR) and the upper
inner fence used to flag outliers?
A. IQR = 30; upper fence = 95 *[CORRECT]*
B. IQR = 30; upper fence = 65
C. IQR = 50; upper fence = 125
D. IQR = 70; upper fence = 95
Correct Answer: A
Rationale: IQR = Q3 − Q1 = 50 − 20 = 30. The 1.5 × IQR rule gives an upper inner fence = Q3 + 1.5 × IQR = 50
+ 45 = 95. Option B uses only Q3 + 0.5 × IQR, while C and D miscompute IQR. The IQR-based fence is the
standard boxplot rule for flagging potential outliers.
BEC1 Statistics Pre-Assessment Page 3
STATISTICS BEC1 STATISTICS PRE
ASSESSMENT 2026/2027
Comprehensive Pre-Assessment Examination — Introductory Statistics
Aligned with BEC1 Statistics Course Syllabus & College-Level Statistics Standards (2026/2027 Edition)
Total Questions: 60 · Sections: 6 · Format: Multiple Choice (4 options, one correct) · Cognitive Mix: 20% Recall,
50% Application, 30% Analysis
Section 1: Descriptive Statistics
Q1: A student recorded the number of hours five classmates spent studying last week: 4, 6,
8, 10, and 12. What is the sample mean of these study hours?
A. 7.0 hours
B. 8.0 hours *[CORRECT]*
C. 9.0 hours
D. 10.0 hours
Correct Answer: B
Rationale: Sum = 4+6+8+10+12 = 40; mean = 40 ÷ 5 = 8.0 hours. Option A divides by the wrong n+1, C and D
reflect miscounted sums. The arithmetic mean of an ungrouped dataset is the sum of observations divided by the
count, a foundational BEC1 descriptive-statistics competency.
Q2: Seven patients reported their systolic blood pressure (mmHg): 118, 122, 124, 125, 127,
130, 145. What is the median blood pressure?
A. 122 mmHg
B. 124 mmHg
C. 125 mmHg *[CORRECT]*
D. 127 mmHg
Correct Answer: C
Rationale: With n = 7 (odd), the median is the middle ordered value, the 4th observation = 125 mmHg. Option A is
Q1, D is close to Q3. The median is resistant to the high outlier (145), illustrating why it is preferred over the mean
for skewed clinical data.
BEC1 Statistics Pre-Assessment Page 1
,STATISTICS BEC1 — Pre-Assessment 2026/2027 60 Questions · Multiple Choice
Q3: A grocery manager counted the daily number of customers buying avocados for a
week: 12, 15, 12, 18, 12, 20, 15. Which of the following correctly describes the mode(s) of
this dataset?
A. 12 only
B. 15 only
C. Both 12 and 15 (bimodal) *[CORRECT]*
D. No mode exists
Correct Answer: C
Rationale: Both 12 and 15 each appear three times — more frequently than any other value — so the dataset is
bimodal. Option A and B each capture only one mode, while D is wrong because at least one value repeats.
Identifying multimodality signals whether a single typical value adequately summarizes the distribution.
Q4: An instructor tells a class: “The range of scores on the midterm was 45 points.” Which
statement is statistically correct?
A. The standard deviation is approximately 45 points.
B. The mean score must have been 45 points.
C. The difference between the highest and lowest score was 45 points. *[CORRECT]*
D. Most students scored within 45 points of the mean.
Correct Answer: C
Rationale: The range is defined as max − min, so a range of 45 means the gap between the highest and lowest
observed scores is 45. Range tells us nothing directly about standard deviation (A), the mean (B), or the spread
around the mean (D). It is the simplest but least stable measure of dispersion.
Q5: A sample of five weekly sales (in units) is: 10, 10, 10, 10, 10. What is the sample
variance?
A. 0 (because every value equals the mean) *[CORRECT]*
B. 1 (the count of distinct values)
C. 10 (the mean itself)
D. Undefined because the data are constant
Correct Answer: A
Rationale: When every observation equals the mean, every deviation is zero, so the sum of squared deviations and
therefore the sample variance s² are both zero. The variance is well-defined and equals zero — there is no spread.
Option D confuses zero variance with division-by-zero; the divisor n − 1 = 4 ≠ 0.
Q6: A dataset has a variance of 49. What is its standard deviation?
A. 7 *[CORRECT]*
B. 24.5
C. 49
D. 2401
Correct Answer: A
Rationale: The standard deviation is the square root of the variance, so √49 = 7. Option B is half of 49, C confuses
standard deviation with variance itself, and D squares 49. Standard deviation returns the measure to the original
units, which is why it is the dispersion measure most often reported in BEC1 coursework.
BEC1 Statistics Pre-Assessment Page 2
, STATISTICS BEC1 — Pre-Assessment 2026/2027 60 Questions · Multiple Choice
Q7: Two production lines report the following: Line A mean = 500 g, standard deviation = 10
g; Line B mean = 1000 g, standard deviation = 15 g. Which line has the greater relative
variability as measured by the coefficient of variation (CV)?
A. Line A (CV = 2.0%) *[CORRECT]*
B. Line B (CV = 1.5%)
C. Both lines have identical CV
D. Cannot be compared because means differ
Correct Answer: A
Rationale: CV = (s / mean) × 100%. Line A: (10/500) × 100% = 2.0%. Line B: (15/1000) × 100% = 1.5%. Despite
Line B having a larger absolute standard deviation, Line A has greater relative variability. CV is the appropriate
tool for comparing dispersion across datasets with different units or magnitudes.
Q8: On a standardized statistics exam scored out of 100, a student's score of 78
corresponds to the 70th percentile. Which interpretation is correct?
A. The student answered 78% of the questions correctly.
B. The student scored higher than 78% of test takers.
C. The student scored higher than 70% of test takers. *[CORRECT]*
D. 70% of the questions were answered correctly.
Correct Answer: C
Rationale: A percentile rank of 70 means the student's score exceeds approximately 70% of all scores in the
reference group. Option A confuses the raw score with a percentage of items correct, B inverts percentile and
score, and D confuses percentile with item-level performance. Percentiles measure relative position, not absolute
correctness.
Q9: For a dataset, Q1 = 20 and Q3 = 50. What are the interquartile range (IQR) and the upper
inner fence used to flag outliers?
A. IQR = 30; upper fence = 95 *[CORRECT]*
B. IQR = 30; upper fence = 65
C. IQR = 50; upper fence = 125
D. IQR = 70; upper fence = 95
Correct Answer: A
Rationale: IQR = Q3 − Q1 = 50 − 20 = 30. The 1.5 × IQR rule gives an upper inner fence = Q3 + 1.5 × IQR = 50
+ 45 = 95. Option B uses only Q3 + 0.5 × IQR, while C and D miscompute IQR. The IQR-based fence is the
standard boxplot rule for flagging potential outliers.
BEC1 Statistics Pre-Assessment Page 3
