# Range Calculator (+ Mean & Median Calculators)

Simply defined, range refers to the difference between a data set’s highest value and the lowest value of the same set. In statistics, the range is important in determining how spread out the values in a given series are. A high range value would indicate that the series is widely spread apart and a small value would indicate that the series has proximity with each other. You can easily calculate the range using this range calculator.

## How to use the range calculator?

Aside from calculating the range, this range calculator also serves as a mean median mode calculator as it can automatically calculate average too. The best thing about this online tool is that it’s very simple and easy to use. To get the values you need, follow these steps:

• For this range and mean calculator, all you have to do is enter two or more Numbers. Separate the values using commas.
• After entering all of the numbers, the tool will automatically provide you with the Mean, Median, Mode, Range, Smallest, Largest, Sum, and Count. It will also Sort the numbers from the smallest to the largest.

## How do you find the range?

Range refers to a measure of dispersion where there’s a likelihood that the values in a data set differ from the mean or the standard. Calculating the range is a simple process. Simply subtract the lowest value from the highest one. You can perform the computation using this formula:

Range = Maximum (xi) – minimum (xi)

where

xi refers to the set of values.

Even without a range calculator, you can manually calculate the range for a certain data set. To do this, follow these steps:

### Make a list of the values in the data set

This is an important first step so you can determine which are the lowest and highest values in the set.

For instance, you have these values in the set: 12, 18, 20, 32, 70, 50.

You can easily identify the lowest and highest values if you list them down in ascending order: 12, 18, 20, 32, 50, 70.

Furthermore, listing them in this order can help when making other calculations, like finding the set’s mean, median or mode.

### Identify the lowest value and the highest value in your set

When arranged in ascending order, the first and last values of the set should be the highest and lowest respectively.

For the example above, the lowest value is 12, and the highest is 70.

### Find the range

To do this, get the difference between the two values:

Range = 70 – 12 = 58

### Clearly label the range

Doing this would avoid any confusion when making other statistical or mathematical calculations which involve using the values of the same set, like when you’re calculating the mean, the median or the mode.

## How do you find range in statistics?

Range may have, or connote, different meanings in mathematics and statistics, but its most basic definition is the difference between the highest and lowest values in a data set. When using the range calculator or the mean median mode calculator, the highest and lowest values of a given data set are required.

Both in statistics and mathematics, the highest and lowest values are the most essential aspects of a data set in terms of calculating the range. As mentioned earlier, you can calculate the range by getting the difference of these two values. Range can give statisticians a better view on how much variation the data set has.

As for the data set itself, there are two essential features that you should always consider namely the data set’s center and the data’s spread. You can measure the center in different ways, and the most common of these are by solving for the mean, midrange, median, and mode. Likewise, there are also different ways in the calculation of the spread of the data set. The most popular and most basic measure of spread is the range.

As aforementioned, solving for the range is pretty straightforward. It’s simply a matter of calculating the difference between the highest and lowest values of the data set. To reiterate with another example, consider these values in a data set, which we’ve arranged in ascending order:  4  12  18  22  25  48  52. Using the formula for range, we can perform the following computation:

Range = 52 – 4 = 48

You can also make use of the range or mean calculator to calculate the average or the range without automatically.

## What is the range of the function?

Functions have both outputs and inputs. The values assigned to the functions are the inputs. What comes out after entering inputs are the outputs. The range of the function refers to the set of outputs of a certain function.  For instance, consider the function of an input raised to the third power. You can represent this using the following equation:

y = x3

Now consider a function with inputs of {-2, -1, 0, 1, 2}. Now we can solve the corresponding outputs. To do this, let’s substitute these inputs for “x” values in the equation:

x = -2               y  =  (-2)3 = -8

x = -1               y  =  (-1)3 = -1

x =  0               y  =   (0)3 = 0

x =  1               y  =   (1)3 = 1

x =  2               y  =   (2)3 = 8

Therefore, the range of values for the input values are {-8, -1, 0, 1, 8} since these correspond to the input values respectively. As this example clearly illustrates, the range of a function is simply the function’s outputs based on the inputs. You can derive the functions in several ways. Here is another example of how to find the range of a function:

Let us consider a drink menu in a restaurant. You can describe this function in words. Using the function rule, let’s assign the following prices to the beverages:

• a small-sized drink may cost \$1.50
• a medium-sized drink may cost \$2.50
• a large-sized drink may cost \$3.50

In this case, the sizes of the drinks are the input, and the prices of the drinks are the output. Since the range of the function involves the set of the outputs, we can, therefore, define the range of the function as {\$1.50, \$2.50, \$3.50}.