Mean, Median, Mode, and Range
A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Measures of center and spread summarize a list of data. The mean balances all values, the median is the middle after ordering, the mode is most common, and the range measures distance from least to greatest. 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
- Compute mean, median, mode, and range
- Choose the summary that matches the question
- Explain how outliers affect mean and range
Worked example
Problem. Find the median of 14, 5, 17, 8, 11.
- Order the data from least to greatest.
- The middle value is 11.
Answer: 11
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: Find the median of 14, 5, 17, 8, 11.
Show solution
- Order the data from least to greatest.
- The middle value is 11.
Answer: 11
2. Practice case B: Find the range of 6, 10, 14, 18, 22.
Show solution
- Range = greatest - least.
- 22 - 6 = 16.
Answer: 16
3. Practice case C: The data set has Q1 = 12 and Q3 = 22. Find the IQR.
Show solution
- IQR = Q3 - Q1.
- 22 - 12 = 10.
Answer: 10
4. Practice case D: Find the mode of 8, 10, 10, 12, 14.
Show solution
- The mode is the value that appears most often.
- 10 appears twice, more than any other value.
Answer: 10
5. Practice case E: Which measure of center is pulled most by one extreme high value?
Choices: Mean · Median · Mode · Sample size
Show solution
- The mean uses every value in the calculation.
- An extreme value can pull the mean upward.
Answer: Mean
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