At a Glance - Range

Let's start with something near and dear to everyone's heart: test scores. Suppose ten students took a math test and received the following scores:

61, 90, 72, 100, 80, 84, 88, 92, 92, 78

It's difficult to make sense out of an unordered list of numbers, so let's start by ordering the list. We'll order the numbers from least to greatest, so they go the same direction as the number line. Also, so that we end on a high note.

61, 72, 78, 80, 84, 88, 90, 92, 92, 100

Since the original list had two copies of the score 92, we keep both copies of 92 in the ordered list also. Each score represents a separate individual, so we don't want to toss someone out just because she tied someone else's score.

Since the scores on the test go from 61 to 100, the difference between the highest and lowest scores is

100 – 61 = 39.

This number, the difference between the highest and lowest values, is called the range of the data.

Exercise 1

Find the range of the following list of test scores. You may want to order each list first.

50, 60, 75, 85, 86, 86, 87.

Exercise 2

Find the range of the following list of test scores. You may want to order each list first.

98, 32, 60, 54, 78, 80, 54, 78, 77, 89.

Exercise 3

Find the range of the following list of test scores. You may want to order each list first.

60, 55, 76, 80, 84, 90, 78, 92.

Exercise 4

Everyone got the same letter grade on the test. Which of the following is more likely to be true?

(a) The range of the test scores was 5.

(b) The range of the test scores was 50.