MATH 225N STATISTICAL REASONING FOR
HEALTH SCIENCES FULL
COMPREHENSIVE FINAL EXAM (3
CREDITS),COURSE CONTENT FOR A
JANUARY 2027 ADMINISTRATION
QUESTIONS AND ANSWERS WITH
RATIONALES
Section 1: Descriptive Statistics (Questions 1–25)
1. A nurse records patient ages: 34, 45, 56, 45, 38, 45, 50. The range is:
A) 11
B) 22
C) 45
D) 56
Answer: B) 22
*Rationale: Range = max(56) − min(34) = 22.*
2. The interquartile range (IQR) measures:
A) The middle 50% of data
B) Total spread
C) Average deviation
D) Skewness
Answer: A) The middle 50% of data
,*Rationale: IQR = Q3 − Q1, robust to outliers.*
3. A health researcher measures the resting heart rates (bpm) of 15 patients: 68, 72, 65, 70, 74, 68,
69, 71, 73, 68, 72, 70, 66, 69, 71. What is the mode?
A) 68
B) 70
C) 71
D) 72
Answer: A) 68
Rationale: 68 appears three times, more than any other value.
4. Which measure of central tendency is most affected by outliers in a clinical data set?
A) Median
B) Mode
C) Mean
D) Range
Answer: C) Mean
Rationale: The mean uses all data points, so extreme values pull it away from the center.
5. For the data set above (Q1), calculate the median. A) 68
B) 69
C) 70
D) 71
Answer: C) 70
Rationale: Sorted: 65,66,68,68,68,69,69,70,70,71,71,72,72,73,74. Middle (8th) is 70.
Section 1: Descriptive Statistics (continued)
,6. In a normal distribution of blood pressure readings, approximately what percentage lies within
±1 standard deviation of the mean?
A) 50%
B) 68%
C) 95%
D) 99.7%
Answer: B) 68%
Rationale: Empirical rule: 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ.
7. The variance of a sample is calculated by dividing the sum of squared deviations by:
A) n
B) n − 1
C) n + 1
D) √n
Answer: B) n − 1
Rationale: Bessel’s correction uses n−1 for unbiased sample variance.
8. A dataset has mean 100 and standard deviation 15. The coefficient of variation (CV) is:
A) 15%
B) 6.67%
C) 85%
D) 150%
Answer: A) 15%
Rationale: CV = (σ/μ)100% = (15/100)*100% = 15%.*
9. Which of the following is NOT a measure of central tendency?
, A) Mean
B) Median
C) Mode
D) Standard deviation
Answer: D) Standard deviation
Rationale: Standard deviation measures spread, not center.
10. A box plot shows the median at 75, Q1 at 60, Q3 at 90. The IQR is:
A) 15
B) 30
C) 75
D) 90
Answer: B) 30
*Rationale: IQR = Q3 − Q1 = 90 − 60 = 30.*
11. In a positively skewed distribution of hospital stay days, the relationship between mean,
median, and mode is: A) Mean < Median < Mode B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mode > Mean > Median
Answer: B) Mean > Median > Mode
Rationale: Positive skew pulls mean to the right.
12. A patient’s cholesterol level is 220 mg/dL. The population mean is 200, SD=20. What is the z-
score?
A) 0.5
B) 1.0
C) 1.5
HEALTH SCIENCES FULL
COMPREHENSIVE FINAL EXAM (3
CREDITS),COURSE CONTENT FOR A
JANUARY 2027 ADMINISTRATION
QUESTIONS AND ANSWERS WITH
RATIONALES
Section 1: Descriptive Statistics (Questions 1–25)
1. A nurse records patient ages: 34, 45, 56, 45, 38, 45, 50. The range is:
A) 11
B) 22
C) 45
D) 56
Answer: B) 22
*Rationale: Range = max(56) − min(34) = 22.*
2. The interquartile range (IQR) measures:
A) The middle 50% of data
B) Total spread
C) Average deviation
D) Skewness
Answer: A) The middle 50% of data
,*Rationale: IQR = Q3 − Q1, robust to outliers.*
3. A health researcher measures the resting heart rates (bpm) of 15 patients: 68, 72, 65, 70, 74, 68,
69, 71, 73, 68, 72, 70, 66, 69, 71. What is the mode?
A) 68
B) 70
C) 71
D) 72
Answer: A) 68
Rationale: 68 appears three times, more than any other value.
4. Which measure of central tendency is most affected by outliers in a clinical data set?
A) Median
B) Mode
C) Mean
D) Range
Answer: C) Mean
Rationale: The mean uses all data points, so extreme values pull it away from the center.
5. For the data set above (Q1), calculate the median. A) 68
B) 69
C) 70
D) 71
Answer: C) 70
Rationale: Sorted: 65,66,68,68,68,69,69,70,70,71,71,72,72,73,74. Middle (8th) is 70.
Section 1: Descriptive Statistics (continued)
,6. In a normal distribution of blood pressure readings, approximately what percentage lies within
±1 standard deviation of the mean?
A) 50%
B) 68%
C) 95%
D) 99.7%
Answer: B) 68%
Rationale: Empirical rule: 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ.
7. The variance of a sample is calculated by dividing the sum of squared deviations by:
A) n
B) n − 1
C) n + 1
D) √n
Answer: B) n − 1
Rationale: Bessel’s correction uses n−1 for unbiased sample variance.
8. A dataset has mean 100 and standard deviation 15. The coefficient of variation (CV) is:
A) 15%
B) 6.67%
C) 85%
D) 150%
Answer: A) 15%
Rationale: CV = (σ/μ)100% = (15/100)*100% = 15%.*
9. Which of the following is NOT a measure of central tendency?
, A) Mean
B) Median
C) Mode
D) Standard deviation
Answer: D) Standard deviation
Rationale: Standard deviation measures spread, not center.
10. A box plot shows the median at 75, Q1 at 60, Q3 at 90. The IQR is:
A) 15
B) 30
C) 75
D) 90
Answer: B) 30
*Rationale: IQR = Q3 − Q1 = 90 − 60 = 30.*
11. In a positively skewed distribution of hospital stay days, the relationship between mean,
median, and mode is: A) Mean < Median < Mode B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mode > Mean > Median
Answer: B) Mean > Median > Mode
Rationale: Positive skew pulls mean to the right.
12. A patient’s cholesterol level is 220 mg/dL. The population mean is 200, SD=20. What is the z-
score?
A) 0.5
B) 1.0
C) 1.5
