Definition: The range of a set of data is the difference between the highest and lowest values in the set.
In the examples below, our first step is to order the data from least to greatest. We recommend that you do this, too. This is especially important with large sets of data. Let's take a closer look.
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: $0.48
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: ^{+}31
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: 5.6 hours
Summary: The range of a set of data is the difference between the highest and lowest values in the set. To find it, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
Exercises
Directions: Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
1. | Find the range of these distances run by 6 marathon runners: 10 km, 15 km, 12 km, 14 km, 8 km, 16 km |
2. | Find the range of these quiz scores: 93, 79, 83, 89, 90, 71, 85 |
3. | Find the range of these race times given in seconds: 7.3 s, 8.4 s, 8.0 s, 7.5 s, 9.4 s, 8.7 s, 9.1 s |
4. | Employees at a retail store are paid the hourly wages listed below. What is the range of these hourly wages? $7.50, $9.25, $8.75, $9.50, $7.25, $8.50 |
5. | In a game, points were won and lost, represented by integers. What is the range of points given below? ^{-}14, ^{+}21, ^{-}17, ^{+}25, 0, ^{-}19, ^{+}11, ^{-}20, ^{+}18 |