The LessonWe can find the range of a set of numbers. Imagine a teacher had set their mathematics class a test. They are concerned that some students are doing much better than others. They wanted to find the range of test scores in the class, to see if some students are doing much better than others.
How to Find the RangeThe range is found by subtracting the lowest number in a set from the highest number.
QuestionWhat is the range of the test scores below?
List the numbers in numerical order (going from the smallest to the largest number).
7 10 8 6 4 → 4 6 7 8 10
Find the lowest number in the set.
4 6 7 8 10The lowest test score is 4.
Find the highest number in the set.
4 6 7 8 10The highest test score is 10.
Subtract the lowest number (4) from the highest number (10).
10 − 4 = 6
Answer:The range of the test scores is 6.
Lesson SlidesThe slider below gives another example of finding the range. Open the slider in a new tab
A Formula to Find the RangeThe formula for finding the range is shown below:
In this formula,
- xmax is the highest number in the set.
- xmin is the lowest number in the set.
How to Find the Range from a Number LineFinding 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 TableSometimes 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. Read more about finding the range from a frequency table
Be Careful When the Lowest Number is NegativeBe 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, 6The 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