Math Math Statistics and Data Analysis 4 — Questions and Answers
Question 1: A dataset has values 12, 15, 15, 18, 20, 22, 50. Which measure of center best represents this data?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
The median is best because the outlier (50) skews the mean, making the median a more representative center.
Question 2: In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
- 68%
- 90%
- 95% (Correct answer)
- 99.7%
Correct answer: 95%
The empirical rule states that approximately 95% of data falls within two standard deviations of the mean in a normal distribution.
Question 3: A survey finds a correlation of r = -0.85 between hours of TV watched and GPA. What does this indicate?
- TV watching causes lower GPA
- There is a strong negative association between the variables (Correct answer)
- There is a weak negative association
- GPA causes less TV watching
Correct answer: There is a strong negative association between the variables
r = -0.85 indicates a strong negative linear association, but correlation does not imply causation.
Question 4: Which sampling method divides the population into groups and randomly selects entire groups?
- Stratified sampling
- Systematic sampling
- Cluster sampling (Correct answer)
- Simple random sampling
Correct answer: Cluster sampling
Cluster sampling divides the population into groups (clusters) and randomly selects entire clusters to survey.
Question 5: A box plot shows Q1 = 30, Q2 = 45, Q3 = 60. What is the interquartile range (IQR)?
- 15
- 30 (Correct answer)
- 45
- 75
Correct answer: 30
IQR = Q3 − Q1 = 60 − 30 = 30.
Question 6: A data set has a mean of 50 and standard deviation of 10. What is the z-score for a value of 35?
- -1.5 (Correct answer)
- -0.5
- 1.5
- 0.5
Correct answer: -1.5
z = (35 − 50) / 10 = −15/10 = −1.5.
Question 7: Which of the following is an example of qualitative (categorical) data?
- Heights of students in inches
- Number of absences per student
- Favorite genre of music (Correct answer)
- Test scores out of 100
Correct answer: Favorite genre of music
Favorite genre of music is categorical data because it represents categories, not numerical measurements.
Math Math Statistics and Data Analysis 4
A dataset has values 12, 15, 15, 18, 20, 22, 50.
Which measure of center best represents this data?