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.
- Worked Example: First identify exactly what the question is asking: Find the median of 14, 5, 17, 8, 11.
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Order the data from least to greatest.
- The middle value is 11.
Answer: 11
Practice problems
1. Practice case A: Find the median of 14, 5, 17, 8, 11.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the median of 14, 5, 17, 8, 11.
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Order the data from least to greatest.
- The middle value is 11.
- Check the result by substituting or estimating: the response should match 11 and make sense in the original problem.
Answer: 11
2. Practice case B: Find the range of 6, 10, 14, 18, 22.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the range of 6, 10, 14, 18, 22.
- For range questions, identify the possible output values after the input restrictions and graph shape are considered.
- Range = greatest - least.
- 22 - 6 = 16.
- Check the result by substituting or estimating: the response should match 16 and make sense in the original problem.
Answer: 16
3. Practice case C: The data set has Q1 = 12 and Q3 = 22. Find the IQR.
Show solution
- Warm-up: First identify exactly what the question is asking: The data set has Q1 = 12 and Q3 = 22. Find the IQR.
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- IQR = Q3 - Q1.
- 22 - 12 = 10.
- Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.
Answer: 10
4. Practice case D: Find the mode of 8, 10, 10, 12, 14.
Show solution
- Warm-up: First identify exactly what the question is asking: Find the mode of 8, 10, 10, 12, 14.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- The mode is the value that appears most often.
- 10 appears twice, more than any other value.
- Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.
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
- Warm-up: First identify exactly what the question is asking: Which measure of center is pulled most by one extreme high value?
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- The mean uses every value in the calculation.
- An extreme value can pull the mean upward.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Mean
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