What is Range in Math? Understanding the Definition and Examples

If you have studied mathematics, you may have come across the term "range." Range is a concept that is often used to describe the spread or variation of a set of numbers. In this article, we will explain what range is and how it can be calculated.

What is Range in Math? Definition

Range is defined as the difference between the largest and smallest values in a set of numbers. To calculate the range, you need to subtract the smallest number from the largest number.

For example, if you have a set of numbers {2, 5, 8, 11, 14}, the smallest number is 2, and the largest number is 14. Therefore, the range is 14 - 2 = 12.

Range is a measure of dispersion or variability, which means it provides information about how spread out the numbers in a set are. A larger range indicates that the data points are more spread out, while a smaller range indicates that the data points are closer together.

Examples of Range in Math

Let's look at some examples to help you understand how range works. Suppose you have the following sets of numbers:

Set A: {2, 4, 6, 8, 10}

Set B: {1, 2, 3, 4, 100}

To calculate the range for Set A, you need to find the difference between the largest and smallest numbers:

Range(A) = 10 - 2 = 8

For Set B, the range is:

Range(B) = 100 - 1 = 99

Notice that Set B has a much larger range than Set A, even though they both have the same number of data points. This is because Set B has an outlier (100), which is much larger than the rest of the numbers in the set. Outliers can significantly affect the range of a set of data.

Example 2:

Suppose you are tracking the daily temperatures in your city for a week, and you have recorded the following temperatures in degrees Celsius: {23, 24, 22, 20, 18, 19, 21}

To calculate the range of temperatures for the week, you need to find the difference between the highest and lowest temperatures:

Range = highest temperature - lowest temperature

In this case, the highest temperature is 24°C, and the lowest temperature is 18°C. So the range of temperatures for the week is:

Range = 24 - 18 = 6°C

This means that the temperatures in your city had a range of 6 degrees Celsius over the course of the week. This information can be useful in many ways, such as predicting weather patterns, evaluating climate conditions, and assessing energy usage.

Conclusion

Range is a measure of variability that helps us understand how spread out the numbers in a set are. It is calculated by finding the difference between the largest and smallest numbers in a set. Understanding range is important in many areas of mathematics and statistics, as it provides valuable information about the data being analyzed.