Range in Statistics: Definition, Uses, and Calculation

You might have come across the word: range a lot. Not just in statistics but almost in every subject. Ever wondered what does it mean? This article will answer all your questions on the range, its calculation, and its uses.

Let’s get started then.

What is Range in Statistics?                                                                            

Here is an example to help you understand this term.

You go shopping every now and then and realize products are sold at a particular price range. You also notice that the store from where you buy your favourite sweater or jeans have a range of size, colour, and fits. This range, which enables us to make a more informed and correct decision, is defined with a lower and upper value and refers to all the units between those values.

Thus, range in math and statistics is known as the difference between the maximum and minimum values of a dataset. The formula of the range is upper value minus/subtracted by the lowest value. This gives researchers and statisticians a better idea of how varied a dataset is.

The spread of the data and the center of the data are two important features of a data set, and the center can be measured in various ways: the most popular are the mean, median, mode, and midrange.  In the same way, there are multiple methods to find out how to spread out the data set is, and the simplest and crudest measure of spread is the range.

How is the Range Calculated?

If you are worried calculating range is as complicated as it sounds, then it is not. In fact, it is one of the easiest formulas you might have ever come across in math or statistics.

Here is the range formula:

Range= Highest Value-Lowest Value

R=H-L

All you need to do is order all the values in the data set in ascending order and then minus or subtract the lowest value from the biggest one. Whether the values you have are negative or positive, even fractions or whole numbers, the process is simply the same.

Suppose your data set is the income of 7 participants.

Income	$300	$250	$800	$100	$160	$900	$660

Now, firstly we will order these participants ranging from low to high incomes.

Income	$100	$160	$250	$300	$660	$800	$900

We will then subtract the lowest salary package from the highest salary package.

R=H-L

R=900-100

Range=800 dollars.

Can you tell a few uses of range now?

Great! Here are some more:

What Are the Uses of Range?

When you have distributions without extremes, range acts as an indicator of variability. If it is paired with measures of central tendency, the range can depict the span of the distribution.

However, the range can be quite misleading if outliers are there in the data set. One extreme value might give you a totally different range in the data.

Below is a range example with an outlier.

Below is a range example with an outlier.

Income	$100	$160	$250	$300	$660	$800	$1900

We get a completely different result with the same calculation.

R=H-L

R=1900-100

1800

So, with an outlier, our range here is $1800.

The range in the sample above shows far more variability in the data than there is. Despite the fact that we have a wide range, the majority of the numbers are grouped around a definite middle.

Outliers can readily sway the range because just two numbers are used.

How is the Range Calculated?

cannot tell you anything about the form of the value distribution on its own.

The range is best used in conjunction with other measures of variability, such as interquartile range and standard deviation, to get a good picture of the variability in your data.