Range (Statistics)

Statistics
definition

Also known as: spread

Grade 6-8

View on concept map

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

Definition

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

💡 Intuition

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

🎯 Core Idea

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

Example

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

Formula

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

Notation

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

🌟 Why It 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.

💭 Hint When Stuck

Circle the largest value and the smallest value in your list, then subtract. That single number is the range.

Formal View

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

🚧 Common Stuck Point

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

⚠️ 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

Frequently Asked Questions

What is Range (Statistics) in Math?

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

What is the Range (Statistics) formula?

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

When do you use Range (Statistics)?

Circle the largest value and the smallest value in your list, then subtract. That single number is the range.

Prerequisites

subtraction

How Range (Statistics) Connects to Other Ideas

To understand range (statistics), you should first be comfortable with subtraction. Once you have a solid grasp of range (statistics), you can move on to standard deviation and interquartile range.

← Back to Explorer