Range Formula

The Formula

\text{range} = \text{maximum} - \text{minimum}

When to use: Range tells you how spread out your data is from end to end. If the tallest kid is 5 feet and the shortest is 4 feet, the range is 1 foot - that's the 'stretch' of heights.

Quick Example

Quiz scores: 72, 85, 90, 68, 95. \text{Range} = 95 - 68 = 27 \text{ points}

Notation

R denotes the range. x_{\max} is the maximum value and x_{\min} is the minimum value in the dataset.

What This Formula Means

The range is the difference between the maximum and minimum values in a data set, giving the simplest measure of overall spread. It tells you the total span of the data from lowest to highest in a single number.

Range tells you how spread out your data is from end to end. If the tallest kid is 5 feet and the shortest is 4 feet, the range is 1 foot - that's the 'stretch' of heights.

Formal View

For a dataset \{x_1, x_2, \ldots, x_n\}, the range is R = x_{\max} - x_{\min} = \max_i(x_i) - \min_i(x_i).

Worked Examples

Example 1

easy
Find the range of the data set: 15, 8, 22, 3, 17.

Solution

  1. 1
    Step 1: Identify the maximum value: 22.
  2. 2
    Step 2: Identify the minimum value: 3.
  3. 3
    Step 3: Range = 22 - 3 = 19.

Answer

19
The range is the simplest measure of spread, calculated as the difference between the largest and smallest values. It gives a quick sense of how spread out the data is.

Example 2

medium
Two basketball players' points per game — Player A: 10, 12, 11, 13, 9. Player B: 5, 20, 8, 18, 4. Who is more consistent?

Common Mistakes

  • Forgetting to subtract
  • Confusing with number of values
  • Ignoring that outliers inflate range

Why This Formula Matters

Range is the simplest measure of spread. It gives a quick sense of how much values vary.

Frequently Asked Questions

What is the Range formula?

The range is the difference between the maximum and minimum values in a data set, giving the simplest measure of overall spread. It tells you the total span of the data from lowest to highest in a single number.

How do you use the Range formula?

Range tells you how spread out your data is from end to end. If the tallest kid is 5 feet and the shortest is 4 feet, the range is 1 foot - that's the 'stretch' of heights.

What do the symbols mean in the Range formula?

R denotes the range. x_{\max} is the maximum value and x_{\min} is the minimum value in the dataset.

Why is the Range formula important in Statistics?

Range is the simplest measure of spread. It gives a quick sense of how much values vary.

What do students get wrong about Range?

Students sometimes report the maximum and minimum as the range instead of computing their difference — range is one number, not two.

What should I learn before the Range formula?

Before studying the Range formula, you should understand: spread vs center.

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