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

compute how much each reported density deviates from the mean, add up all the deviations,

and then take their average. Table 19.4 shows the deviation from the mean for each reported

density. As one can see, the sum of the deviations is zero for both groups. This is not a coinci-

dence. In fact, the sum of deviations from the mean for any given sample is always zero. This

can be readily verified by considering the following:

(19.1)

(19.2)

wherexirepresents data points, is the average,nis the number of data points, anddirepre-

sents the deviation from average.

x

di 1 xix 2

x

1

na

n

i 1

xi

19.4 Measures of Central Tendency and Variation —Mean, Median, and Standard Deviation 639

TABLE 19.3 Reported Densities of Water at 20C

Group A Findings Group B Findings

r(kg /m

3

) r(kg /m

3

)

1020 950

1015 940

990 890

1060 1080

1030 1120

950 900

975 1040

1020 1150

980 910

960 1020

ravg 1000 ravg 1000

TABLE 19.4 Deviations from the Mean

Group A Group B

R (RRavg) |(RRavg)| R (RRavg) |(RRavg)|

1020  20 20 950  50 50

1015  15 15 940  60 60

990  10 10 890  110 110

1060  60 60 1080  80 80

1030  30 30 1120  120 120

950  50 50 900  100 100

975  25 25 1040  40 40

1020  20 20 1150  150 150

980  20 20 910  90 90

960  40 40 1020  20 20

g 0 g 290 g 0 g 820

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