Range Calculator (for Statistical Data)

This calculator finds the **statistical range** for a set of numbers. Enter your data below, separated by commas, spaces, or new lines, and click "Calculate" to find the range, maximum, and minimum values.

Note: This tool calculates the statistical range (Max - Min). It does not find the range of a function (e.g., $f(x) = x^2$), which is a different concept.

What is the Range in Statistics?

In statistics, the **range** is the simplest and most straightforward measure of variability or "spread" in a data set. It is defined as the difference between the largest (maximum) value and the smallest (minimum) value in the set.

While easy to calculate, the range is highly sensitive to outliers (unusually large or small values) and doesn't provide information about the distribution of the data between the two extremes.

How to Calculate the Range

The formula for the range is:

To find the range manually, follow these simple steps:

1. List your data: Gather all the numbers in your data set.
2. Sort the data (Optional): It's easiest to find the maximum and minimum values by sorting your data set from smallest to largest.
3. Identify the Maximum (Max): Find the largest number in the set.
4. Identify the Minimum (Min): Find the smallest number in the set.
5. Subtract: Subtract the minimum value from the maximum value to get the range.

Example Calculation

Let's find the range for the following data set: {10, 3, 42, 17, 9, 3, 22}

1. Data Set: {10, 3, 42, 17, 9, 3, 22}
2. Sorted Set: {3, 3, 9, 10, 17, 22, 42}
3. Maximum (Max): 42
4. Minimum (Min): 3
5. Calculate Range: $42 - 3 = 39$

The range for this data set is 39.

Range of a Function vs. Range of a Data Set

It's important not to confuse the **statistical range** of a data set with the **range of a function** in algebra.

• Statistical Range (This Calculator): The difference between the max and min values in a list of numbers. Example: For {2, 5, 9}, the range is 7.
• Function Range (Algebra): The set of all possible *output* values (y-values) a function can produce. Example: For the function $f(x) = x^2$, the range is all non-negative numbers, or $[0, \infty)$.

This tool is designed for the first definition: the statistical range of a data set.

Frequently Asked Questions (FAQ)