FAST Descriptive Statistics 3 — Questions and Answers
Question 1: A dataset's mean is 50 and standard deviation is 10. A value of 70 has a z-score of:
- 1.5
- 2 (Correct answer)
- 0.2
- 20
Correct answer: 2
Z = (value − mean) / SD = (70 − 50) / 10 = 20 / 10 = 2.
Question 2: The heights (cm) of 5 students are: 160, 165, 170, 175, 180. What is the mean absolute deviation (MAD)?
- 6 (Correct answer)
- 8
- 10
- 5
Correct answer: 6
Mean = 170; absolute deviations: 10, 5, 0, 5, 10; MAD = 30/5 = 6.
Question 3: In a dataset, the 90th percentile value means:
- 90% of values are above it
- The value equals 90
- 90% of values fall at or below it (Correct answer)
- The value is 90% of the maximum
Correct answer: 90% of values fall at or below it
The nth percentile is the value below which n% of the data falls.
Question 4: Which of the following best describes a leptokurtic distribution compared to a normal distribution?
- Flatter with lighter tails
- Taller peak with heavier tails (Correct answer)
- Perfectly symmetric
- Bimodal with two peaks
Correct answer: Taller peak with heavier tails
Leptokurtic distributions have positive excess kurtosis, meaning a sharper peak and heavier tails than a normal distribution.
Question 5: Data: 3, 7, 7, 2, 9, 3, 7. What is the mode?
- 3
- 7 (Correct answer)
- 2
- Both 3 and 7
Correct answer: 7
7 appears three times, which is more than any other value, making it the mode.
Question 6: A researcher reports a coefficient of variation (CV) of 5% for Dataset A and 40% for Dataset B. This means:
- Dataset A has higher absolute variability
- Dataset B is more consistent relative to its mean
- Dataset A is more consistent relative to its mean (Correct answer)
- Both datasets have equal spread
Correct answer: Dataset A is more consistent relative to its mean
CV = (SD/mean) × 100%; a lower CV indicates less relative variability, so Dataset A (5%) is more consistent.
Question 7: When constructing a stem-and-leaf plot for the values 23, 27, 31, 35, 38, the stems would be:
- 2, 3 (Correct answer)
- 23, 27, 31
- 0, 10, 20, 30
- 3, 7, 1, 5, 8
Correct answer: 2, 3
For two-digit numbers in the 20s and 30s, the tens digits (2 and 3) serve as stems.
FAST Descriptive Statistics 3
A dataset's mean is 50 and standard deviation is 10.
A value of 70 has a z-score of: