Civil Engineering Reference
In-Depth Information
Figure 9.1
Simulated distribution of test results.
Table 9.1
Percentage of results
outside statistical
limits
A (%)
k
0.1
3.09
1.0
2.33
2.5
1.96
5.0
1.65
10
1.28
table of figures (ordinates) appearing in any statistics textbook. This table
will be accompanied by a second table (Table 9.1) listing the areas under
the graph more than a given distance away from the mean (the high point).
The information needed to construct the graph (apart from the table of
figures) is only the mean (average) of all the results, which we shall call
X, and a quantity called σ or SD, which is the standard deviation and is a
measure of how widely the results are spread. The numbers X and σ can
be read from many simple calculators when a series of results are entered;
a computer can also automatically produce them. The standard deviation is
the square root of the average of the squares of all the differences between
each individual result and the average of all results, that is,
σ =
√
[∑ (
x
i
-
x
m
)
2
/n]
where
x
i
= Individual result
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