Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

19.3 Frequency Distributions 637

Frequency

10

8

6

4

2

0

50–59 60–69 70–79 80–89 90–99

Scores

■Figure 19.1

The histogram for the scores

given in Table 19.1.

TABLE 19.2 Cumulative Frequency Distribution for Example 19.2

Range Frequency Cumulative Frequency

50 –59 3 3 3

60 – 69 5 3  5  88

70 –79 9 3  5  9 17 or 8  9  17 17

80 – 89 6 3  5  9  6 23 or 17  6  23 23

90 – 99 3 3  5  9  6  3 26 or 23  3  26 26

Cumulative Frequency

The data can be organized further by calculating thecumulative frequency. The cumulative fre-

quency shows the cumulative number of students with scores up to and including those in the

given range. We have calculated the cumulative frequency for Example 19.2 and shown it in

Table 19.2. For Example 19.2, eight scores fall in the range of 50 to 69, and 17 students’ scores

(the majority of the class) show an average or below-average performance.

The cumulative frequency distribution can also be displayed using a histogram or a

cumulative frequency polygon, as shown in Figures 19.2 and 19.3, respectively. These figures

Cumulative Frequency

30

25

20

15

10

5

0

50–59 50–69 50–79 50–89 50–99

Scores

■Figure 19.2

The cumulative-frequency

histogram for Example 19.2.

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