Data Variability Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Data Variability.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

How much the values in a data set are spread out or clustered together around the center.

Two archery targets both have average hits at the bullseye. But one archer's arrows are scattered all over, while the other's are clustered tightly. Same average, very different consistency. That difference is variability.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Two data sets can have the same average but completely different spreads. Variability captures the consistency or inconsistency of the data.

Common stuck point: Students focus only on the average and ignore spread, missing crucial information about how reliable or predictable the data is.

Worked Examples

Example 1

easy
Two classes took the same test. Class A scores: 70, 72, 68, 71, 69. Class B scores: 50, 90, 60, 80, 70. Both have a mean of 70. Which class has more variability?

Solution

  1. 1
    Step 1: Class A range: 72 - 68 = 4. Class B range: 90 - 50 = 40.
  2. 2
    Step 2: A larger range indicates the data is more spread out.
  3. 3
    Step 3: Class B has much more variability (range 40 vs 4).

Answer

Class B has more variability.
Variability measures how spread out data values are. Two data sets can have the same mean but very different variability, which tells us how consistent or inconsistent the values are.

Example 2

medium
Daily temperatures (°C) for a week: 20, 22, 19, 21, 20, 23, 21. Calculate the mean and describe the variability informally.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Set X: {5, 5, 5, 5, 5}. Set Y: {1, 3, 5, 7, 9}. Both have mean 5. Which set has zero variability and why?

Example 2

easy
Team A scores 14, 15, 15, 16, 15 in five games. Team B scores 10, 15, 20, 15, 15. Which team has greater variability? Explain briefly.
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Related Concepts

Mean as Fair Share

Background Knowledge

These ideas may be useful before you work through the harder examples.

mean fair sharenumber comparison