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

636 Chapter 19 Probability and Statistics in Engineering

19.3 Frequency Distributions

As we have said repeatedly throughout the text, engineers are problem solvers. They apply phys-

ical laws, chemical laws, and mathematics to design, develop, test, and supervise the manufac-

ture of millions of products and services. Engineers perform tests to learn how things behave or

how well they are made. As they perform experiments, they collect data that can be used to

explain certain things better and to reveal information about the quality of products and services

they provide. In the previous section, we defined what we mean by population and samples. In

general, any statistical analysis starts with identifying the population and the sample. Once we

have defined a sample that represents the population and have collected information about the

sample, then we need to organize the data in a certain way such that pertinent information and

conclusions can be extracted. To shed light on this process, consider the following example.

Example 19.2 The scores of a test for an introductory chemistry class of 26 students are shown here. Cer-

tainly, the scores of your class would be better than these! We are interested in drawing some

conclusions about how good this class is. The scores of a test for Example 19.2:

Scores:58, 95, 80, 75, 68, 97, 60, 85, 75, 88, 90, 78, 62, 83, 73, 70, 70, 85, 65, 75, 53, 62,

56, 72, 79

As you can see from the way the data (scores) are represented, we cannot easily draw a con-

clusion about how good this chemistry class is. One simple way of organizing the data better

would be to identify the lowest and the highest scores, and then group the data into equal inter-

vals or ranges: say a range of size 10, as shown in Table 19.1. When data is organized in the man-

ner shown in Table 19.1, it is commonly referred to as agrouped frequency distribution.

TABLE 19.1 Grouped Frequency Distribution for Example 19.2

Scores Range Frequency

58, 53, 56 50 –59 3

68, 60, 62, 65, 62 60 – 69 5

75, 75, 78, 73, 70, 70, 75, 72, 79 70 –79 9

80, 85, 88, 83, 85, 87 80 – 89 6

95, 97, 90 90 – 99 3

The way the scores are now organized in Table 19.1 reveals some useful information. For

example, three students did poorly and three performed admirably. Moreover, nine students

received scores that were in the range of 70 –79, which is considered an average performance.

These average scores also constitute the largest frequency in the given data set. Another useful

piece of information, which is clear from examining Table 19.1, is that the frequency (the num-

ber of scores in a given range) increases from 3 to 5 to 9 and then decreases from 6 to 3. Another

way of showing the range of scores and their frequency is by using abar graph(what is com-

monly called ahistogram). The height of the bars shows the frequency of the data within the

given ranges. The histogram for Example 19.2 is shown in Figure 19.1.

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