## 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.