# Range In Math — Definition, How To Find & Examples

Written by
Malcolm McKinsey
Fact-checked by
Paul Mazzola

## What is range?

In math, range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest. In a set of data, the range is the difference between the greatest and smallest value.

Range is one of four simple tools of statistics:

• Mean – The arithmetic mean of a set of numbers is its average (the sum of the numbers divided by the quantity of numbers)

• Median – The statistical median is the middle number in an ordered set of numbers

• Mode – The mode is the most commonly occurring number in a data set

• Range – The range of a data set is the mathematical difference between the largest and smallest value

The first three statistical tools are measures of central tendency, or how similar the numbers are.

Only range is a measure of dispersion, highlighting how different the numbers are, and there is a simple formula to calculate range.

### Range formula

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## How to find range

To find the range in a set of numbers, you must gather your data, organize the data from least to greatest, then subtract the smallest value from the largest value. You can find a range of positive numbers and negative numbers.

Steps for how to calculate range:

1. Gather your data, so you know all the numbers to be studied.

2. Arrange the data set in order from least to greatest.

3. Write a subtraction sentence to subtract the smallest value from the greatest (or largest) value.

For example, if you read a biography, and wrote down how many pages you read each day, you could take the range:

• Monday – 12 pages

• Tuesday – 9 pages

• Wednesday – 11 pages

• Thursday – 3 pages

• Friday – 8 pages

To find the range, put the number of pages in order from least to greatest:

Subtract the smallest value from the greatest value:

The range of this data set is 9 pages.

### How to find the range between two numbers

The range is typically used to find the dispersion of values in a data set comprising several values. However, you don’t need all the other numbers to find the range between two numbers.

Finding the range between two numbers is the same as finding the range of a set of data. For example, say you have a data set of just two numbers: 10 and 4

The greatest number is 10 and the lowest number is 4. So, 10 - 4 = 6

The range between these two numbers is 6.

## Range examples

Let's look at some example problems and figure the range. Below are five of the lowest-scoring games in NBA history, listed with teams and total game points:

• Washington Capitols (49) vs. Pittsburgh Ironmen (40) – 89 points

• Fort Wayne Pistons (19) vs. Minneapolis Lakers (18) – 37 points

• Washington Capitols (50) vs. Detroit Falcons (33) – 83 points

• Boston Celtics (46) vs. Pittsburgh Ironmen (44) – 90 points

• Boston Celtics (47) vs. Washington Capitols (38) – 85 points

Go through the three steps to find the range of these five games:

Step 1: Gather your data points, so you know all the numbers to be studied

Step 2: Arrange the data set in order from least to highest number

Step 3: Subtract the smallest value from the highest value to get your range

The range of the five lowest-scoring games in NBA history is 53 points!

Let's try this with some more challenging numbers, like country populations.

• China has an estimated population of 1,420,062,022 people.

• Mexico's population is 132,328,035.

• India has a population of 1,368,737,513.

• The United States has a population of 329,093,110.

What is the range of this data set?

To get our answer we gather the data and arrange the data in order from least to greatest:

1. 132,328,035

2. 329,093,100

3. 1,368,737,513

4. 1,420,062,022

Then, subtract the smallest value from the greatest value:

The range of this data set, or difference between the population of Mexico and China, is 1,287,733,987 people!

## Using range in real life

Range is used in real life to make mathematical calculations. Range can be used to calculate the amount of time that has passed, like when calculating your age.

The current year is 2020, and you were born in 2005. How old are you? Or how much time has passed?

15 years have passed, so if your 2020 birthday has already passed, then you are 15 years old. Range is also used in real life to figure out the dispersion of a high school class' test scores, to determine the price range for a service, and much more.

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