how to find the range of data

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 data from the everyman to the highest value in the distribution. It is a ordinarily used measure of variability.

Along with measures of cardinal tendency, measures of variability requite you descriptive statistics for summarizing your data prepare.

The range is calculated by subtracting the lowest value from the highest value. While a big range means loftier variability, a modest range means depression variability in a distribution.

Calculate 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 calculate. To find the range, follow these steps:

Society all values in your data set from low to high.
Subtract the everyman value from the highest value.

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

Range case

Your data ready is the ages of 8 participants.

Participant	1	two	3	4	5	vi	seven	eight
Age	37	19	31	29	21	26	33	36

Starting time, social club the values from depression to loftier to identify the lowest value (50) and thehighest value (H).

Historic period	19	21	26	29	31	33	36	37

So subtract the lowest from the highest value.

R = H – L

R = 37 – 19 = eighteen

The range of our data set is 18 years.

How useful is the range?

The range generally gives you lot a good indicator of variability when yous have a distribution without extreme values. When paired with measures of central tendency, the range tin can tell y'all almost the span of the distribution.

But the range tin be misleading when you have outliers in your information fix. One extreme value in the data will give you a completely different range.

Range example with an outlier

One value in your data set is replaced with an outlier.

Historic period	19	21	26	29	31	33	36	61

Using the same calculation, nosotros get a very unlike result this time:

R = H – L

R = 61 – 19 = 42

With an outlier, our range is now 42 years.

In the example above, the range indicates much more variability in the information than in that location really is. Although we have a big range, almost values are actually clustered around a articulate middle.

Because only two numbers are used, the range is easily influenced past outliers. It can't tell you about the shape of the distribution of values on its own.

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

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