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

642 Chapter 19 Probability and Statistics in Engineering

TABLE 19.7 Evaluating Midpoints of Data and xf

Range Frequencyf Midpointxxf

50 –59 3 54.5 163.5

60 – 69 5 64.5 322.5

70 –79 9 74.5 670.5

80 – 89 6 84.5 507

90 – 99 3 94.5 283.5

ngf 26 gxf 1947

g

Using Equation (19.7), the mean of the scores is

Similarly, using Equation (19.8), we calculate the standard deviation, as shown in Table 19.8.

Normal distribution is discussed next.

s

B

g 1 xx 2

2

f

n 1



B

3496

25

11.8

n 1  25

n g f 26

x

g 1 x f 2

n



1947

26

74.9

TABLE 19.8 Computing Standard Deviation

Frequency Midpoint

Range fx

50 –59 3 54.5 74.9 20.4 1248.5

60 – 69 5 64.5 74.9 10.4 540.8

70 –79 9 74.5 74.9 0.4 1.44

80 – 89 6 84.5 74.9 9.6 552.96

90 – 99 3 94.5 74.9 19.6 1152.5

(x )

2

g x f 3496

1 xx 2

2

x xx f

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