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Statistics · Centre and spread

How to Find the Range of a Data Set

Problem

12,\ 7,\ 15,\ 3,\ 9

Answer

\text{range } 12

The range is the simplest measure of spread. It tells you how wide the whole data set is.

Step-by-step solution

Find the largest value.
$15$
Why: The range starts at the top of the data set.
Find the smallest value.
$3$
Why: The range ends at the bottom of the data set.
Subtract the smallest from the largest.
$15 - 3 = 12$
Why: The range is one number: the spread of the data.

Common mistakes

Subtracting the largest from the smallest. The range cannot be negative.
Reporting two values. The range is a single number.
Calling the range the mean. The mean is a centre value.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$5,\ 9,\ 2$

Show answer

$\text{range } 7$
$10,\ 20,\ 15$

Show answer

$\text{range } 10$
$4,\ 4,\ 4$

Show answer

$\text{range } 0$
$1,\ 100$

Show answer

$\text{range } 99$
$8,\ 6,\ 13,\ 7$

Show answer

$\text{range } 7$