Range (Statistics) Formula

The Formula

\text{Range} = \text{Maximum} - \text{Minimum}

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

Quick Example

Temperatures: 65°, 72°, 68°, 80°, 71°. \text{Range} = 80 - 65 = 15°

Notation

R = x_{\max} - x_{\min}

What This Formula Means

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.

Formal View

R = x_{(n)} - x_{(1)} where x_{(1)} = \min_i x_i and x_{(n)} = \max_i x_i

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.

Common Mistakes

  • Computing maximum plus minimum instead of maximum minus minimum
  • Assuming two data sets with the same range have similar distributions — one could be clustered, the other spread
  • Forgetting that a single outlier can inflate the range dramatically and misrepresent the typical spread

Why This Formula Matters

The range provides an instant, simple measure of variability — though it is sensitive to outliers, it is useful as a first check on data spread.

Frequently Asked Questions

What is the Range (Statistics) formula?

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

How do you use the Range (Statistics) formula?

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

What do the symbols mean in the Range (Statistics) formula?

R = x_{\max} - x_{\min}

Why is the Range (Statistics) formula important in Math?

The range provides an instant, simple measure of variability — though it is sensitive to outliers, it is useful as a first check on data spread.

What do students get wrong about Range (Statistics)?

Range can be misleading—two data sets with same range can look very different.

What should I learn before the Range (Statistics) formula?

Before studying the Range (Statistics) formula, you should understand: subtraction.

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