Comparing Distributions
A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Comparing distributions means comparing shape, center, spread, and outliers together. A good comparison says which group is higher or more variable and uses the context of the data. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Compare centers and spreads
- Use shape and outliers in a comparison
- Write a complete comparative statement
Worked example
Problem. A larger standard deviation means the data values are generally:
- Standard deviation measures typical distance from the mean.
- Larger standard deviation means more spread.
Answer: farther from the mean
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: A larger standard deviation means the data values are generally:
Choices: farther from the mean · closer to the median · all equal · categorical labels
Show solution
- Standard deviation measures typical distance from the mean.
- Larger standard deviation means more spread.
Answer: farther from the mean
2. Practice case B: Which display shows median, quartiles, and range at once?
Choices: Scatter plot · Two-way table · Pie chart · Box plot
Show solution
- A box plot is built from the five-number summary.
- It shows median, quartiles, and overall range.
Answer: Box plot
3. Practice case C: When comparing two distributions, a complete comparison should mention:
Choices: only the sample size · only the graph title · shape, center, spread, and unusual values · only the largest number
Show solution
- Comparisons should address the full distribution.
- Shape, center, spread, and unusual values give the clearest comparison.
Answer: shape, center, spread, and unusual values
4. Practice case D: One group has range 8 and another has range 13. How much larger is the second range?
Show solution
- Compare the two spreads by subtracting.
- 13 - 8 = 5.
Answer: 5
5. Practice case E: An outlier is best described as:
Choices: a value far from the overall pattern · the middle value · the total number of values · a required part of every sample
Show solution
- Outliers are unusually far from the rest of the data.
- They can affect center and spread.
Answer: a value far from the overall pattern
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