638 Chapter 19 Probability and Statistics in Engineering
convey the same information as contained in Table 19.2. However, it might be easier for some
people to absorb the information when it is presented graphically. Engineers use graphical com-
munication when it is the clearer, easier and more convenient way to convey information.19.4 Measures of Central Tendency and Variation–
Mean, Median, and Standard Deviation
In this section, we will discuss some simple ways to examine the central tendency and variations
within a given data set. Every engineer should have some understanding of the basic funda-
mentals of statistics and probability for analyzing experimental data and experimental errors.
There are always inaccuracies associated with all experimental observations. If several variables
are measured to compute a final result, then we need to know how the inaccuracies associated
with these intermediate measurements will influence the accuracy of the final result. There are
basically two types of observation errors: systematic errors and random errors. Suppose you
were to measure the boiling temperature of pure water at sea level and standard pressure with
a thermometer that reads 104C. If readings from this thermometer are used in an experiment,
it will result in systematic errors. Therefore,systematic errors, sometimes calledfixed errors,
are errors associated with using an inaccurate instrument. These errors can be detected and
avoided by properly calibrating instruments. On the other hand,random errorsare generated
by a number of unpredictable variations in a given measurement situation. Mechanical vibra-
tions of instruments or variations in line voltage friction or humidity could lead to fluctuations
in experimental observations. These are examples of random errors.
Suppose two groups of students in an engineering class measured the density of water at
20 C. Each group consisted of ten students. They reported the results shown in Table 19.3. We
would like to know if any of the reported data is in error.
Let us first consider themean(arithmetic average) for each group’s findings. The mean of
densities reported by each group is 1000 kg /m
3. The mean alone cannot tell us whether any
student or which student(s) in each group may have made a mistake. What we need is a way of
defining the dispersion of the reported data. There are a number of ways to do this. Let us
Cumulative Frequency
30
25
20
15
10
5
0
50 60 70 80 90 100Scores
■Figure 19.3
The cumulative-frequency
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