Range

Measures Of Spread
definition

Also known as: range

Grade 3-5

View on concept map

The range is the difference between the maximum and minimum values in a data set, giving the simplest measure of overall spread. Range is the simplest measure of spread.

Definition

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.

💡 Intuition

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.

🎯 Core Idea

Range measures the total span of the data from lowest to highest. A single extreme outlier can make range misleadingly large.

Example

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

Formula

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

Notation

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

🌟 Why It Matters

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

💭 Hint When Stuck

First, find the largest value (maximum) in your data set. Then find the smallest value (minimum). Finally, subtract: Range = Maximum - Minimum. Remember, the range is one number, not a pair of numbers.

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).

Compare With Similar Concepts

Mean vs MedianRange vs Interquartile Range

🚧 Common Stuck Point

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

⚠️ Common Mistakes

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

Frequently Asked Questions

What is Range in Statistics?

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.

What is the Range formula?

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

When do you use Range?

First, find the largest value (maximum) in your data set. Then find the smallest value (minimum). Finally, subtract: Range = Maximum - Minimum. Remember, the range is one number, not a pair of numbers.

Prerequisites

spread vs center

How Range Connects to Other Ideas

To understand range, you should first be comfortable with spread vs center. Once you have a solid grasp of range, you can move on to variability intro and stat interquartile range.

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