In statistics, the **range** represents the difference between the smallest and largest value in a dataset.

For example, suppose we have the following dataset:

Dataset: 3, 4, 11, 15, 19, 19, 19, 22, 22, 23, 23, 26

We can use the following formula to calculate the range:

- Range = Maximum value – Minimum value
- Range = 26 – 3
- Range = 23

The range is **23**. This represents the difference between the smallest and largest values in the dataset.

In statistics, the range is important for the following reasons:

**Reason 1**: It tell us the spread of the entire dataset.

**Reason 2**: It tells us what extreme values are possible in a given dataset.

The following examples illustrate each of these reasons in practice.

**Reason 1: The Range Tells Us the Spread of an Entire Dataset**

The range tells us the spread of an entire dataset.

For example, suppose we have the following dataset that shows the exam scores of 20 different students in a class:

The range for the exam scores would be calculated as:

- Range = Maximum value – Minimum value
- Range = 98 – 68
- Range = 30

The range turns out to be **30**. This represents the difference between the highest exam score and the lowest exam score in the class.

Knowing just this metric, the teacher of the class can gain a quick understanding of the spread of values in exam scores among all of the students.

**Reason 2: The Range tells us what extreme values are possible in a given dataset**

The range tells us what extreme values are possible in a given dataset.

For example, suppose a realtor has access to a database that contains the selling price of 100,000 houses in a certain city in the United States:

Suppose we use some statistical software (like Excel, R, Python, etc.) to calculate the range of this dataset and find the following:

- Range = Maximum Value – Minimum Value
- Range = 854,000 – 194,000
- Range = 660,000

If the realtor has a client who has a purchasing budget of less than $194,000 or greater than $854,000, the realtor can immediately know that there will be no houses in this particular city that meet the purchasing criteria.

**The Drawback of Using the Range**

The range suffers from one drawback: **It is influenced by outliers**.

To illustrate this, consider the following dataset:

**Dataset:** 1, 4, 8, 11, 13, 17, 19, 19, 20, 23, 24, 24, 25, 28, 29, 31, 32

The range of this dataset is 32 – 1 = **31**.

However, consider if the dataset had one extreme outlier:

**Dataset:** 1, 4, 8, 11, 13, 17, 19, 19, 20, 23, 24, 24, 25, 28, 29, 31, 32, **378**

The range of this dataset would now be 378 – 1 = **377**.

Notice how the range changes dramatically as a result of one outlier.

Before calculating the range of any dataset, it’s a good idea to first check if there are any outliers that could cause the range to be misleading.

**Additional Resources**

The following tutorials explain the importance of other metrics in statistics:

Why is the Mean Important in Statistics?

Why is the Median Important in Statistics?

Why is the Mode Important in Statistics?

Why is Standard Deviation Important in Statistics?