Shape, Center, Spread, and Outliers
A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.
A useful statistical description mentions more than one number. Shape tells what the distribution looks like, center tells where typical values live, spread tells how much values vary, and outliers warn that one value may change the story. 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
- Describe a distribution using shape, center, and spread
- Identify possible outliers
- Choose resistant summaries when data is skewed
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: categorical labels · farther from the mean · closer to the median · all equal
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: Two-way table · Pie chart · Box plot · Scatter 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 largest number · only the sample size · only the graph title · shape, center, spread, and unusual values
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 required part of every sample · a value far from the overall pattern · the middle value · the total number of values
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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