Problem: Cheryl took 7 math tests in one marking period. What is the range of her test scores?
89, 73, 84, 91, 87, 77, 94
Solution: Ordering the test scores from least to greatest, we get:
73, 77, 84, 87, 89, 91, 94
highest - lowest = 94 - 73 = 21
Answer: The range of these test scores is 21 points.
Definition: The range of a set of data is the difference between the highest and lowest values in the set.
In the problem above, the set of data consists of 7 test scores. We ordered the data from least to greatest before finding the range. We recommend that you do this, too. This is especially important with large sets of data. Let's look at some more 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.
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.
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.
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.
Exercises
Directions: Find the range of each set of data. 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 |