College Math Placement Test Statistics 3 — Questions and Answers
Question 1: A boxplot shows Q1 = 20, median = 35, Q3 = 50. What is the interquartile range (IQR)?
- 15
- 30 (Correct answer)
- 35
- 25
Correct answer: 30
IQR = Q3 − Q1 = 50 − 20 = 30.
Question 2: Which of the following describes a negatively skewed distribution?
- Mean > Median > Mode
- Mean = Median = Mode
- Mean < Median < Mode (Correct answer)
- Mode > Mean > Median
Correct answer: Mean < Median < Mode
In a negatively (left) skewed distribution, the mean is pulled toward the tail, so Mean < Median < Mode.
Question 3: A correlation coefficient of r = −0.92 indicates:
- A weak positive relationship
- No relationship
- A strong negative relationship (Correct answer)
- A moderate positive relationship
Correct answer: A strong negative relationship
A value of −0.92 is close to −1, indicating a strong negative linear relationship.
Question 4: A student rolls a fair die twice. What is the probability of getting a 6 on both rolls?
- 1/6
- 1/36 (Correct answer)
- 1/12
- 2/6
Correct answer: 1/36
Since the rolls are independent, P(6 and 6) = 1/6 × 1/6 = 1/36.
Question 5: A survey asks 200 people about their preferred genre. The results are displayed in a pie chart. If 30% prefer drama, how many people prefer drama?
- 30
- 60 (Correct answer)
- 70
- 15
Correct answer: 60
30% of 200 = 0.30 × 200 = 60 people.
Question 6: What does a z-score of −2 tell you about a data point?
- It is 2 units below the mean
- It is 2 standard deviations below the mean (Correct answer)
- It is 2% below the median
- It is below the mode by 2
Correct answer: It is 2 standard deviations below the mean
A z-score represents how many standard deviations a value is from the mean; −2 means 2 standard deviations below.
Question 7: Which sampling method divides a population into subgroups and randomly selects from each subgroup?
- Simple random sampling
- Cluster sampling
- Systematic sampling
- Stratified sampling (Correct answer)
Correct answer: Stratified sampling
Stratified sampling divides the population into strata (subgroups) and samples from each stratum.
College Math Placement Test Statistics 3
A boxplot shows Q1 = 20, median = 35, Q3 = 50.
What is the interquartile range (IQR)?