## How to Find the Range

The range is found by subtracting the lowest number in a set from the highest number.## Question

What is the range of the test scores below?## Step-by-Step:

## 1

List the numbers in numerical order (going from the smallest to the largest number).

7 10 8 6 4 → 4 6 7 8 10

## 2

Find the lowest number in the set.
The lowest test score is 4.

**4**6 7 8 10

## 3

Find the highest number in the set.

4 6 7 8

The highest test score is 10.
**10**## 4

Subtract the lowest number (4) from the highest number (10).

10 − 4 = 6

## Answer:

The range of the test scores is 6.## A Formula to Find the Range

The formula for finding the range is shown below:In this formula,**x**is the highest number in the set._{max}**x**is the lowest number in the set._{min}

## How to Find the Range from a Number Line

Finding the range of a set of numbers on a number line is easy. If we plot the test scores on a number line (with the highest and lowest scores in red), the range is the distance between the highest and lowest numbers on the number line:The range is the distance between the highest and lowest numbers on the number line. In our example, it is 6.## How to Find the Range from a Frequency Table

Sometimes data is presented in frequency tables. A frequency table representing the test scores is shown below:It is possible to find that the range of the test scores is 6. Learn more about finding the range from a frequency table

## Beware

## Be Careful When the Lowest Number is Negative

Be careful when the lowest number in a set is a negative number. Let's find the range of the following numbers:
−2, 0, 3, 4, 6

The range is found by subtracting the lowest number (−2) from the highest number (6):
Range = 6 − (−2)

**Don't forget:**Subtracting a negative number is equivalent to adding the (positive) number. (

*Two negatives make a positive!*) Subtracting −2 is equivalent to adding (+)2:

Range = 6 − (−2) = 6 + (+2) = 6 + 2

Range = 8

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