how do you find range in math

How to Find the Range of a Data Set | Formula & Examples

Published on September 11, 2020 by Pritha Bhandari. Revised on September 25, 2020.

In statistics, the range is the spread of your information from the lowest to the highest value in the distribution. Information technology is a commonly used measure of variability.

Along with measures of key tendency, measures of variability give you descriptive statistics for summarizing your data set up.

The range is calculated by subtracting the lowest value from the highest value. While a large range ways high variability, a small range means low variability in a distribution.

Summate the range

The formula to calculate the range is:

Formula to find the range

R = range
H = highest value
L = lowest value

The range is the easiest measure of variability to summate. To find the range, follow these steps:

Order all values in your data set from depression to high.
Subtract the lowest value from the highest value.

This process is the same regardless of whether your values are positive or negative, or whole numbers or fractions.

Range case

Your information set is the ages of 8 participants.

Participant	ane	2	3	4	5	vi	vii	8
Age	37	nineteen	31	29	21	26	33	36

First, order the values from low to high to identify the lowest value (L) and thehighest value (H).

Age	19	21	26	29	31	33	36	37

Then subtract the everyman from the highest value.

R = H – L

R = 37 – 19 = 18

The range of our data set is eighteen years.

How useful is the range?

The range generally gives you a good indicator of variability when you take a distribution without farthermost values. When paired with measures of central tendency, the range can tell you about the bridge of the distribution.

Only the range can exist misleading when you take outliers in your data set. Ane extreme value in the information will give you a completely different range.

Range case with an outlier

1 value in your information gear up is replaced with an outlier.

Historic period	19	21	26	29	31	33	36	61

Using the same adding, we become a very different result this time:

R = H – 50

R = 61 – 19 = 42

With an outlier, our range is at present 42 years.

In the example higher up, the range indicates much more variability in the data than there actually is. Although nosotros take a large range, virtually values are really clustered around a clear middle.

Considering only ii numbers are used, the range is easily influenced past outliers. Information technology tin can't tell you about the shape of the distribution of values on its own.

To get a clear idea of your data'southward variability, the range is all-time used in combination with other measures of variability like interquartile range and standard deviation.