Range (Statistics) Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Range (Statistics).

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

Concept Recap

The statistical range is the difference between the maximum and minimum values in a data set: \text{range} = \max - \min.

The range answers "how spread out is the data from end to end?" — it captures the total span but ignores everything in between.

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: Range only uses two values—it ignores everything in between.

Common stuck point: Range can be misleading—two data sets with same range can look very different.

Sense of Study hint: Circle the largest value and the smallest value in your list, then subtract. That single number is the range.

Worked Examples

Example 1

easy
Find the range of the data set: \{3, 7, 2, 9, 5, 1, 8\}.

Solution

  1. 1
    Identify the maximum value: \max = 9
  2. 2
    Identify the minimum value: \min = 1
  3. 3
    Apply the range formula: \text{Range} = \max - \min = 9 - 1 = 8

Answer

\text{Range} = 8
The range measures the total spread of a data set by subtracting the smallest value from the largest value. A larger range indicates greater variability in the data.

Example 2

medium
Two classes took the same test. Class A scores: \{55, 70, 85, 90, 95\}. Class B scores: \{72, 74, 76, 78, 80\}. Compare the ranges and explain what the difference tells you.

Practice Problems

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

Example 1

easy
Find the range of the monthly temperatures (°F): \{32, 45, 58, 72, 85, 90, 88, 75, 62, 48, 36, 30\}.

Example 2

hard
A data set has a range of 24. If the maximum value is 3x + 5 and the minimum value is x - 3, find the value of x.
← Back to Range (Statistics) Formula Explained Practice Mode

Background Knowledge

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

subtraction