Statistics Descriptive Statistics & Data Summarization 2 — Questions and Answers
Question 1: Which statistic is most appropriate for describing the center of a heavily skewed income distribution?
- Median (Correct answer)
- Mean
- Mode
- Standard deviation
Correct answer: Median
The median is resistant to skewness and extreme values, making it ideal for skewed distributions.
Question 2: What does a box plot's whisker typically represent?
- 1.5 × IQR beyond the quartiles (Correct answer)
- The minimum and maximum values
- One standard deviation from the mean
- The 10th and 90th percentiles
Correct answer: 1.5 × IQR beyond the quartiles
By convention, box plot whiskers extend to 1.5 times the IQR beyond Q1 and Q3.
Question 3: What is the coefficient of variation (CV) used for?
- Comparing variability between datasets with different units or means (Correct answer)
- Measuring the correlation between two variables
- Describing the shape of a distribution
- Calculating the range of a dataset
Correct answer: Comparing variability between datasets with different units or means
The CV expresses standard deviation as a percentage of the mean, enabling comparison across different scales.
Question 4: In a symmetric bell-shaped distribution, which of the following is true?
- Mean = Median = Mode (Correct answer)
- Mean > Median > Mode
- Mode > Median > Mean
- Mean < Median < Mode
Correct answer: Mean = Median = Mode
In a perfectly symmetric unimodal distribution, all three measures of center are equal.
Question 5: Which of the following best describes a stem-and-leaf plot?
- A display that preserves original data values while showing distribution shape (Correct answer)
- A chart comparing categorical frequencies
- A graph of cumulative probabilities
- A plot of two quantitative variables
Correct answer: A display that preserves original data values while showing distribution shape
A stem-and-leaf plot retains actual data values while simultaneously showing the shape of the distribution.
Question 6: What does a z-score of −2 indicate about a data point?
- It is 2 standard deviations below the mean (Correct answer)
- It is 2 standard deviations above the mean
- It is 2 units below the median
- It falls in the 2nd percentile
Correct answer: It is 2 standard deviations below the mean
A z-score measures how many standard deviations a value is from the mean; negative means below.
Statistics Descriptive Statistics & Data Summarization 2
Which statistic is most appropriate for describing the center of a heavily skewed income distribution?