Data Science Statistical Concepts and Analysis 3 — Questions and Answers
Question 1: Which sampling method gives every member of a population an equal chance of selection?
- Simple random sampling (Correct answer)
- Convenience sampling
- Quota sampling
- Snowball sampling
Correct answer: Simple random sampling
Simple random sampling ensures each unit has an identical probability of being chosen.
Question 2: The standard deviation measures:
- The typical spread of values around the mean (Correct answer)
- The middle value of a dataset
- The most frequent value
- The difference between max and min
Correct answer: The typical spread of values around the mean
Standard deviation quantifies average dispersion of data points from the mean.
Question 3: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 68% (Correct answer)
- 50%
- 95%
- 99.7%
Correct answer: 68%
The empirical rule states about 68% of values lie within ±1 standard deviation.
Question 4: Which is an example of a categorical (nominal) variable?
- Eye color (Correct answer)
- Temperature in Celsius
- Annual income
- Height in centimeters
Correct answer: Eye color
Eye color labels categories with no inherent numeric order, making it nominal.
Question 5: If two events are mutually exclusive, then:
- They cannot occur at the same time (Correct answer)
- They are independent
- Their probabilities multiply
- They always occur together
Correct answer: They cannot occur at the same time
Mutually exclusive events have no overlap, so they cannot both happen simultaneously.
Question 6: What does R-squared represent in a regression model?
- The proportion of variance in the outcome explained by predictors (Correct answer)
- The slope of the regression line
- The correlation between residuals
- The number of predictors used
Correct answer: The proportion of variance in the outcome explained by predictors
R-squared is the fraction of the dependent variable's variance accounted for by the model.
Question 7: A boxplot's interquartile range (IQR) spans which values?
- The 25th to the 75th percentile (Correct answer)
- The minimum to the maximum
- The 10th to the 90th percentile
- The mean plus or minus one SD
Correct answer: The 25th to the 75th percentile
The IQR is the distance between Q1 (25th) and Q3 (75th) percentiles, covering the middle 50%.
Data Science Statistical Concepts and Analysis 3
Which sampling method gives every member of a population an equal chance of selection?