How to Find the Range with Negative Numbers

Statistics · Centre and spread

How to Find the Range with Negative Numbers

Problem

4,\ -2,\ -7,\ 3

Answer

\text{range } 11

The range is always largest minus smallest. With negative numbers, subtracting a negative adds, which is where most sign errors happen.

Step-by-step solution

Find the largest value.
$4$
Why: On the number line, 4 is the furthest right.
Find the smallest value.
$-7$
Why: Negative seven is the furthest left.
Subtract the smallest from the largest.
$4 - (-7) = 4 + 7 = 11$
Why: Subtracting a negative number adds its size.

Common mistakes

Using -7 as the range because it is the largest digit.
Computing 4 - 7 = -3 and losing the sign.
Subtracting in the other order: -7 - 4 = -11.

Practice problems

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

$5,\ -3,\ 0,\ 2$

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$\text{range } 8$
$-1,\ -8,\ -4$

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$\text{range } 7$
$6,\ -6$

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$\text{range } 12$
$-5,\ 2,\ -9,\ 1$

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$\text{range } 11$
$0,\ -10,\ 5$

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$\text{range } 15$