Applied Statistics and Probability for Engineers

192 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION

EXAMPLE 6-2 Table 6-1 displays the quantities needed for calculating the sample variance and sample

standard deviation for the pull-off force data. These data are plotted in Fig. 6-2. The

numerator of is

so the sample variance is

and the sample standard deviation is

Computation of s^2

The computation of requires calculation of , nsubtractions, and nsquaring and adding op-

erations. If the original observations or the deviations are not integers, the deviations

xixmay be tedious to work with, and several decimals may have to be carried to ensure

xix

s^2 x

s 1 0.22860.48 pounds

s^2 

1.60

8  1



1.60

7

0.2286 1 pounds 22

a

8

i 1

1 xix 22 1.60

s^2

x 4 x 5

x 7

x

x 6

x 1 x 3

x 2 x 8

12 13 14 15

Figure 6-2 How the

sample variance meas-

ures variability through

the deviations xix.

Table 6-1 Calculation of Terms for the Sample Variance and Sample

Standard Deviation

i

1 12.6 0.4 0.16

2 12.9 0.1 0.01

3 13.4 0.4 0.16

4 12.3 0.7 0.49

5 13.6 0.6 0.36

6 13.5 0.5 0.25

7 12.6 0.4 0.16

8 13.1 0.1 0.01

104.0 0.0 1.60

xi xix 1 xix 22

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