# Why is the Range Important in Statistics?

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.