Data Science Statistical Concepts and Inference 3 — Questions and Answers
Question 1: For a strongly right-skewed income distribution, which measure of central tendency best represents a typical value?
- Mean
- Median (Correct answer)
- Mode
- Range
Correct answer: Median
The median is resistant to extreme values and better reflects the typical observation in skewed data.
Question 2: A correlation coefficient of -0.9 indicates:
- A weak negative relationship
- A strong negative linear relationship (Correct answer)
- No relationship
- A strong positive relationship
Correct answer: A strong negative linear relationship
A coefficient near -1 indicates a strong negative linear association.
Question 3: Which statement about correlation and causation is correct?
- Correlation implies causation
- A high correlation proves one variable causes the other
- Correlation can arise from a confounding variable without direct causation (Correct answer)
- Causation requires zero correlation
Correct answer: Correlation can arise from a confounding variable without direct causation
Two variables can be correlated due to a lurking confounder rather than one causing the other.
Question 4: In a normal distribution, approximately what percentage of values fall within two standard deviations of the mean?
- 68%
- 95% (Correct answer)
- 99.7%
- 50%
Correct answer: 95%
The empirical rule states about 95% of data lies within two standard deviations of the mean.
Question 5: A z-score of 0 means the observation is:
- Two standard deviations above the mean
- Exactly at the mean (Correct answer)
- An outlier
- Below the median
Correct answer: Exactly at the mean
A z-score of 0 indicates the value equals the mean.
Question 6: Which sampling method gives every member of the population an equal chance of selection?
- Convenience sampling
- Simple random sampling (Correct answer)
- Snowball sampling
- Quota sampling
Correct answer: Simple random sampling
Simple random sampling ensures each unit has an equal and independent probability of selection.
Question 7: The interquartile range (IQR) measures:
- The difference between the maximum and minimum
- The spread of the middle 50% of the data (Correct answer)
- The average distance from the mean
- The most frequent value
Correct answer: The spread of the middle 50% of the data
The IQR is the distance between the 25th and 75th percentiles, capturing the central half of the data.
Data Science Statistical Concepts and Inference 3
For a strongly right-skewed income distribution, which measure of central tendency best represents a typical value?