Problem: Cheryl took 7 math tests in a marking period. What is the range of your test scores?

89, 73, 84, 91, 87, 77, 94

Solution: By sorting the test scores from minimum to maximum, you get:

73, 77, 84, 87, 89, 91, 94

maximum – minimum = 94 – 73 = 21

Answer: The range of scores for these tests is 21 points.

Definition: The range of a data set is the difference between the highest and lowest values in the set.

In the above problem, the data set consists of 7 test scores. We sorted the data from minimum to maximum before we found the range. We recommend doing this as well. This is particularly important in case of large data sets. Let’s see some other examples.

Jumping with GasExample 1: The Jaeger family crossed 6 states in the Midwest during the summer vacation. Gas 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: Sorting the data from minimum to maximum, we get:

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

maximum – minimum = \$2.09 – \$1.61 = \$0.48

Answer: The range of gasoline prices is \$0.48.

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

14, -12, 7, 0, -5, -8, 17, -11, 19

Solution: Sorting the data from minimum to maximum, 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.

MarathonExample 3: A marathon was completed by 5 participants. What is the time interval indicated in hours?

2.7 hours, 8.3 hours, 3.5 hours, 5.1 hours, 4.9 hours

Solution: Sorting the data from minimum to maximum, we get:

2.7, 3.5, 4.9, 5.1, 8.3

maximum – minimum = 8.3 hours – 2.7 hours = 5.6 hours

Answer: The swimming time interval is 5.6 hours.

Summary: The interval of a data set is the difference between the highest and lowest value of the set. To find the range, first sort the data from minimum to maximum. Then subtract the smallest value from the largest value in the set.