Statistics BEC1 Pre-Assessment 2026/2027 60 Questions | 6 Sections
STATISTICS BEC1 STATISTICS PRE
ASSESSMENT 2026/2027
Comprehensive Pre-Assessment Examination - 60 Multiple-Choice Questions
This pre-assessment examination is designed to evaluate foundational competency in introductory statistics as outlined in
the BEC1 Statistics course syllabus. The exam consists of 60 multiple-choice questions distributed across six core
sections: Descriptive Statistics; Probability and Probability Distributions; Sampling and Data Collection Methods;
Confidence Intervals and Hypothesis Testing; Correlation and Regression Analysis; and Chi-Square and Non-Parametric
Tests. Each question carries one mark, and the suggested time allocation is approximately 90 minutes. Cognitive levels
span recall, application, and analysis, mirroring college-level introductory statistics standards (2026/2027 edition).
Section 1: Descriptive Statistics
*Q1:* A researcher records the number of hours that eight undergraduate students spent studying
statistics in a week: 5, 8, 12, 6, 9, 11, 7, 10. What is the mean number of study hours?
A. 8.0 hours
B. 8.5 hours *[CORRECT]*
C. 9.0 hours
D. 9.5 hours
Correct Answer: B
Rationale: The mean equals the sum of all observations divided by the count. The sum is 5+8+12+6+9+11+7+10 =
68, and = 8.5. Option A divides by 9 (an off-by-one error), C rounds the sum incorrectly, and D adds an extra
phantom value to the data set.
*Q2:* A clinic recorded the resting heart rate (beats per minute) of seven patients: 72, 68, 75, 80, 70,
74, 76. What is the median heart rate?
A. 72
B. 73
C. 74 *[CORRECT]*
D. 75
Correct Answer: C
Rationale: First sort the data: 68, 70, 72, 74, 75, 76, 80. With n = 7 (odd), the median is the middle value at position
(n+1)/2 = 4, which is 74. Options A, B, and D reflect common errors such as failing to sort the data, picking the wrong
middle position, or averaging the wrong pair of values.
*Q3:* An instructor records the number of students absent over 10 sessions: 2, 0, 1, 2, 3, 2, 0, 4, 2, 1.
Which of the following is the modal number of absences?
A. 0
B. 1
C. 2 *[CORRECT]*
D. 3
Correct Answer: C
BEC1 Statistics - Pre-Assessment Exam Page 1
,Statistics BEC1 Pre-Assessment 2026/2027 60 Questions | 6 Sections
Rationale: The mode is the value that appears most frequently. The value 2 occurs four times, more than any other
value, so the mode is 2. The values 0, 1, and 3 occur less frequently and reflect either averaging the data or mistakenly
picking the lowest or middle value as the mode.
*Q4:* A sample of five daily temperatures (in degrees Celsius) is recorded: 20, 22, 24, 26, 28. What is
the sample standard deviation?
A. 2.83
B. 3.16 *[CORRECT]*
C. 4.00
D. 5.10
Correct Answer: B
Rationale: The sample standard deviation uses divisor (n-1). The mean is 24; the squared deviations sum to
4+4+0+4+16 = 40; dividing by (n-1) = 4 gives 10, and sqrt(10) is approximately 3.16. Option A divides by n (the
population SD), while C and D reflect arithmetic slips in either the squared deviations or the square-root step.
*Q5:* A dataset has values 4, 8, 6, 10, 12. What is the sample variance?
A. 8.0
B. 10.0 *[CORRECT]*
C. 12.5
D. 16.0
Correct Answer: B
Rationale: The mean is 8. The squared deviations are 16, 0, 4, 4, 16, summing to 40. The sample variance is 40 / (5-1)
= = 10.0. Option A wrongly divides by n = 5 (giving the population variance), C mixes up the divisor, and D
doubles the correct result.
*Q6:* Two machines produce bottles. Machine A has mean fill 500 mL with SD 5 mL; Machine B has
mean fill 250 mL with SD 4 mL. Which machine is relatively more variable?
A. Machine A, because it has the larger SD
B. Machine B, because its coefficient of variation is larger *[CORRECT]*
C. They are equally variable because both SDs are small
D. Cannot be compared without the full data set
Correct Answer: B
Rationale: Coefficient of variation (CV) = (SD / mean) x 100%. Machine A: (5/500) x 100% = 1.0%; Machine B:
(4/250) x 100% = 1.6%. Machine B is relatively more variable, even though its absolute SD is smaller, illustrating why
CV is preferred when means differ in scale.
*Q7:* A student scores 68 on an exam where scores are approximately normally distributed with mean
75 and standard deviation 6. The student's score corresponds to which approximate percentile?
A. 8th percentile
B. 12th percentile *[CORRECT]*
C. 38th percentile
D. 88th percentile
Correct Answer: B
BEC1 Statistics - Pre-Assessment Exam Page 2
, Statistics BEC1 Pre-Assessment 2026/2027 60 Questions | 6 Sections
Rationale: z = (68 - 75) / 6 = -1.17. The cumulative probability below z = -1.17 is approximately 0.121, so the student
is at roughly the 12th percentile. Option A uses z = -1.5 (a wrong z), C uses the area above rather than below, and D is
the upper-tail area for a positive z.
*Q8:* In a normally distributed dataset with mean 100 and standard deviation 15, what is the z-score
for a value of 130?
A. 1.0
B. 1.5
C. 2.0 *[CORRECT]*
D. 2.5
Correct Answer: C
Rationale: z = (x - mu) / sigma = (130 - 100) / 15 = = 2.0. Option A subtracts incorrectly, B divides by 20, and
D adds an extra 0.5. A z-score of 2.0 places the value 2 standard deviations above the mean.
*Q9:* A histogram of student test scores is shown with a long tail extending to the left (toward lower
scores). Which statement best describes the distribution?
A. Symmetric, so mean equals median
B. Right-skewed, so mean exceeds median
C. Left-skewed, so mean is less than median *[CORRECT]*
D. Bimodal, with two visible peaks
Correct Answer: C
Rationale: A histogram with a long tail to the left is left-skewed (negatively skewed). In left-skewed distributions, the
mean is pulled toward the tail and is less than the median. The other options confuse the direction of skewness or
assume symmetry where there is none.
*Q10:* A boxplot displays the five-number summary for weekly sales (in thousands of dollars): Min =
20, Q1 = 35, Median = 45, Q3 = 60, Max = 85. Which statement correctly interprets the interquartile
range (IQR)?
A. IQR = 65, calculated as Max - Min
B. IQR = 25, calculated as Q3 - Q1 *[CORRECT]*
C. IQR = 15, calculated as Median - Q1
D. IQR = 40, calculated as Q3 - Min
Correct Answer: B
Rationale: The IQR measures the spread of the middle 50% of data and is computed as Q3 - Q1 = 60 - 35 = 25. Option
A uses the full range, C uses the wrong pair (median and Q1), and D incorrectly mixes Q3 with the minimum value.
*Q11:* A stem-and-leaf plot shows the stems 5, 6, 7 with leaves: stem 5 has 2, 4, 8; stem 6 has 1, 3, 9;
stem 7 has 0, 5. How many observations are in the dataset?
A. 5
B. 6
C. 8 *[CORRECT]*
D. 10
Correct Answer: C
BEC1 Statistics - Pre-Assessment Exam Page 3
STATISTICS BEC1 STATISTICS PRE
ASSESSMENT 2026/2027
Comprehensive Pre-Assessment Examination - 60 Multiple-Choice Questions
This pre-assessment examination is designed to evaluate foundational competency in introductory statistics as outlined in
the BEC1 Statistics course syllabus. The exam consists of 60 multiple-choice questions distributed across six core
sections: Descriptive Statistics; Probability and Probability Distributions; Sampling and Data Collection Methods;
Confidence Intervals and Hypothesis Testing; Correlation and Regression Analysis; and Chi-Square and Non-Parametric
Tests. Each question carries one mark, and the suggested time allocation is approximately 90 minutes. Cognitive levels
span recall, application, and analysis, mirroring college-level introductory statistics standards (2026/2027 edition).
Section 1: Descriptive Statistics
*Q1:* A researcher records the number of hours that eight undergraduate students spent studying
statistics in a week: 5, 8, 12, 6, 9, 11, 7, 10. What is the mean number of study hours?
A. 8.0 hours
B. 8.5 hours *[CORRECT]*
C. 9.0 hours
D. 9.5 hours
Correct Answer: B
Rationale: The mean equals the sum of all observations divided by the count. The sum is 5+8+12+6+9+11+7+10 =
68, and = 8.5. Option A divides by 9 (an off-by-one error), C rounds the sum incorrectly, and D adds an extra
phantom value to the data set.
*Q2:* A clinic recorded the resting heart rate (beats per minute) of seven patients: 72, 68, 75, 80, 70,
74, 76. What is the median heart rate?
A. 72
B. 73
C. 74 *[CORRECT]*
D. 75
Correct Answer: C
Rationale: First sort the data: 68, 70, 72, 74, 75, 76, 80. With n = 7 (odd), the median is the middle value at position
(n+1)/2 = 4, which is 74. Options A, B, and D reflect common errors such as failing to sort the data, picking the wrong
middle position, or averaging the wrong pair of values.
*Q3:* An instructor records the number of students absent over 10 sessions: 2, 0, 1, 2, 3, 2, 0, 4, 2, 1.
Which of the following is the modal number of absences?
A. 0
B. 1
C. 2 *[CORRECT]*
D. 3
Correct Answer: C
BEC1 Statistics - Pre-Assessment Exam Page 1
,Statistics BEC1 Pre-Assessment 2026/2027 60 Questions | 6 Sections
Rationale: The mode is the value that appears most frequently. The value 2 occurs four times, more than any other
value, so the mode is 2. The values 0, 1, and 3 occur less frequently and reflect either averaging the data or mistakenly
picking the lowest or middle value as the mode.
*Q4:* A sample of five daily temperatures (in degrees Celsius) is recorded: 20, 22, 24, 26, 28. What is
the sample standard deviation?
A. 2.83
B. 3.16 *[CORRECT]*
C. 4.00
D. 5.10
Correct Answer: B
Rationale: The sample standard deviation uses divisor (n-1). The mean is 24; the squared deviations sum to
4+4+0+4+16 = 40; dividing by (n-1) = 4 gives 10, and sqrt(10) is approximately 3.16. Option A divides by n (the
population SD), while C and D reflect arithmetic slips in either the squared deviations or the square-root step.
*Q5:* A dataset has values 4, 8, 6, 10, 12. What is the sample variance?
A. 8.0
B. 10.0 *[CORRECT]*
C. 12.5
D. 16.0
Correct Answer: B
Rationale: The mean is 8. The squared deviations are 16, 0, 4, 4, 16, summing to 40. The sample variance is 40 / (5-1)
= = 10.0. Option A wrongly divides by n = 5 (giving the population variance), C mixes up the divisor, and D
doubles the correct result.
*Q6:* Two machines produce bottles. Machine A has mean fill 500 mL with SD 5 mL; Machine B has
mean fill 250 mL with SD 4 mL. Which machine is relatively more variable?
A. Machine A, because it has the larger SD
B. Machine B, because its coefficient of variation is larger *[CORRECT]*
C. They are equally variable because both SDs are small
D. Cannot be compared without the full data set
Correct Answer: B
Rationale: Coefficient of variation (CV) = (SD / mean) x 100%. Machine A: (5/500) x 100% = 1.0%; Machine B:
(4/250) x 100% = 1.6%. Machine B is relatively more variable, even though its absolute SD is smaller, illustrating why
CV is preferred when means differ in scale.
*Q7:* A student scores 68 on an exam where scores are approximately normally distributed with mean
75 and standard deviation 6. The student's score corresponds to which approximate percentile?
A. 8th percentile
B. 12th percentile *[CORRECT]*
C. 38th percentile
D. 88th percentile
Correct Answer: B
BEC1 Statistics - Pre-Assessment Exam Page 2
, Statistics BEC1 Pre-Assessment 2026/2027 60 Questions | 6 Sections
Rationale: z = (68 - 75) / 6 = -1.17. The cumulative probability below z = -1.17 is approximately 0.121, so the student
is at roughly the 12th percentile. Option A uses z = -1.5 (a wrong z), C uses the area above rather than below, and D is
the upper-tail area for a positive z.
*Q8:* In a normally distributed dataset with mean 100 and standard deviation 15, what is the z-score
for a value of 130?
A. 1.0
B. 1.5
C. 2.0 *[CORRECT]*
D. 2.5
Correct Answer: C
Rationale: z = (x - mu) / sigma = (130 - 100) / 15 = = 2.0. Option A subtracts incorrectly, B divides by 20, and
D adds an extra 0.5. A z-score of 2.0 places the value 2 standard deviations above the mean.
*Q9:* A histogram of student test scores is shown with a long tail extending to the left (toward lower
scores). Which statement best describes the distribution?
A. Symmetric, so mean equals median
B. Right-skewed, so mean exceeds median
C. Left-skewed, so mean is less than median *[CORRECT]*
D. Bimodal, with two visible peaks
Correct Answer: C
Rationale: A histogram with a long tail to the left is left-skewed (negatively skewed). In left-skewed distributions, the
mean is pulled toward the tail and is less than the median. The other options confuse the direction of skewness or
assume symmetry where there is none.
*Q10:* A boxplot displays the five-number summary for weekly sales (in thousands of dollars): Min =
20, Q1 = 35, Median = 45, Q3 = 60, Max = 85. Which statement correctly interprets the interquartile
range (IQR)?
A. IQR = 65, calculated as Max - Min
B. IQR = 25, calculated as Q3 - Q1 *[CORRECT]*
C. IQR = 15, calculated as Median - Q1
D. IQR = 40, calculated as Q3 - Min
Correct Answer: B
Rationale: The IQR measures the spread of the middle 50% of data and is computed as Q3 - Q1 = 60 - 35 = 25. Option
A uses the full range, C uses the wrong pair (median and Q1), and D incorrectly mixes Q3 with the minimum value.
*Q11:* A stem-and-leaf plot shows the stems 5, 6, 7 with leaves: stem 5 has 2, 4, 8; stem 6 has 1, 3, 9;
stem 7 has 0, 5. How many observations are in the dataset?
A. 5
B. 6
C. 8 *[CORRECT]*
D. 10
Correct Answer: C
BEC1 Statistics - Pre-Assessment Exam Page 3
