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

The standard deviation for a grouped distribution is calculated from

(19.8)

Next, we demonstrate the use of these formulas.

Example 19.3 For Example 19.2, using Equations (19.7) and (19.8), calculate the mean and standard devia-

tion of the class scores.

Consult Tables 19.6, 19.7, and 19.8, respectively, while following the solution. To calcu-

late the mean, first we need to evaluate the midpoints of data for each range and then evaluate

the gxfas shown.

s

B

g 1 xx 2

2

f

n 1

19.4 Measures of Central Tendency and Variation –Mean, Median, and Standard Deviation 641

TABLE 19.6 Data for Example 19.3

Range Frequency

50 –59 3

60 – 69 5

70 –79 9

80 – 89 6

90 – 99 3

TABLE 19.5 Standard Deviation Calculation for Each Group

Group A Group B

(rravg)

2

(rravg)

2

400 2500

225 3600

100 12,100

3600 6400

900 14,400

2500 10,000

625 1600

400 22,500

400 8100

1600 400

s34.56 (kg /m

3

) s95.22 (kg /m

3

)

g10,750 g81,600

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