how to find the range in math

How to Find the Range of a Information Gear up | 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.

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

The range is calculated past subtracting the lowest value from the highest value. While a large range means high variability, a small range ways low 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 = everyman value

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

Order all values in your data set from low 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 example

Your data set is the ages of 8 participants.

Participant	1	2	three	four	5	6	vii	viii
Age	37	19	31	29	21	26	33	36

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

Age	nineteen	21	26	29	31	33	36	37

Then subtract the lowest from the highest value.

R = H – 50

R = 37 – 19 = 18

The range of our data set is xviii years.

How useful is the range?

The range generally gives you a proficient indicator of variability when you lot have a distribution without extreme values. When paired with measures of central tendency, the range can tell you about the span of the distribution.

But the range tin can be misleading when you have outliers in your information gear up. One farthermost value in the data will give yous a completely different range.

Range example with an outlier

1 value in your information set is replaced with an outlier.

Age	19	21	26	29	31	33	36	61

Using the same calculation, we go a very different result this time:

R = H – 50

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 data than there really is. Although we have a large range, most values are actually clustered effectually a clear middle.

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

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

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