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Range

We've already seen some measures of central tendency, such as mean, median, and mode. Here, we'll see range.

Think of the range of a function like its spread. How big is the difference between the largest and smallest values (real numbers) in the data set?

To calculate range, subtract the minimum value in the data set from the maximum value. So, that means $\text{maximum value - minimum value}$.

Make sure to put the values of your data set in order BEFORE you try to find the range. That makes it much easier to find out what the highest number and lowest numbers are.

Sets of data with bigger differences between their smallest and largest value have bigger ranges.

Sets of data with smaller differences between their smallest and largest value have smaller ranges.

$$\text{Range = largest value - smallest value} = 14-7=\boxed{7}$$

So, the range is $7.$

Let's do another example!

$$\text{Range = largest value - smallest value} = 900-106=\boxed{794}$$

So, the range is $794.$

Follow these simple steps to solve for range with any data set.

(Video) Mean, Median, Mode, and Range

by MathHelp.com

MathHelp.com has a great video explaining how to find the mean, median, mode, and range.

We are going to focus on range in this explanation, but you can also review explanations in mean, median, and mode.

$\large{\text{Summary}}$

From any given data set we can find all four quantities. The range is the the lowest number in the set subtracted from the highest number in the set. Let's look at the following set.

$$8, 6, 19, -5, -4, 7, 18.$$

As always, the first step is to write the numbers in the data set in increasing order.

Now we can find the range.

$$\text{Range = largest value - smallest value} = 19 - (-5) = 24$$

If you need to review subtracting negative numbers, check out this lesson.

Range

To find the range of a data set, subtract the smallest value from the largest value. $$\text{range} = \text{largest value}-\text{smallest value}$$

To find the range of the data set $-3, 67, 1000, -1000$ let's first put the values in order so we can easily find the largest and smallest values. $$-1000, -3, 67, 1000$$

The largest value is $1000$ and the smallest value is $-1000.$ Now, let's find the range!

$$\text{range} = \text{largest value}-\text{smallest value} = 1000-(-1000) = \boxed{2000}$$