Definition of Range

How to Find the Range in Math?

The Range is the difference between the lowest and highest values.

Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9.

So the range is 9 − 3 = 6.

It is that simple!

But perhaps too simple …

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The Range Can Be Misleading

The range can sometimes be misleading when there are extremely high or low values.

Example: In {8, 11, 5, 9, 7, 6, 3616}:

• the lowest value is 5,
• and the highest is 3616,

So the range is 3616 − 5 = 3611.
The single value of 3616 makes the range large, but most values are around 10.

Examples

Example 1: The Jaeger family drove through 6 midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the range of gasoline prices?

$1.79,  $1.61,  $1.96,  $2.09,  $1.84,  $1.75

Solution: Ordering the data from least to greatest, we get:

$1.61,  $1.75,  $1.79,  $1.84,  $1.96,  $2.09

highest – lowest = $2.09 – $1.61 = $0.48

Answer: The range of gasoline prices is $0.48.

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Example 2: Ms. Kaiser listed 9 integers on the blackboard. What is the range of these integers?

14,  ^–12,  7,  0,  ^–5,  ^–8,  17,  ^–11,  19

Solution: Ordering the data from least to greatest, we get:

^–12,  ^–11,  ^–8,  ^–5,  0,  7,  14,  17,  19

highest – lowest = 19 – ^–12 = 19 + ⁺12 = ⁺31

Answer: The range of these integers is ⁺31.

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Example 3: A marathon race was completed by 5 participants. What is the range of times given in hours below?

2.7 hr,  8.3 hr,  3.5 hr,  5.1 hr,  4.9 hr

Solution: Ordering the data from least to greatest, we get:

2.7,  3.5,  4.9,  5.1,  8.3

highest – lowest = 8.3 hr – 2.7 hr = 5.6 hr

Answer: The range of swim times is 5.6 hr.

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Summary: The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

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