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9 Guide to statistics
All measurements are subject to some uncertainties. Even if all systematic sources of uncertainty are
identified and eliminated, randomness remains inevitably inherent. In most measurements, as the number
of observations increase, a relatively large number of observations will be found close to the mean value.
As the number of observations the approaches infinity, their distribution approaches a continuous curve
hereafter referred to as the normal distribution.
Figure 1 illustrates two sets of observations with the s
ame mean value and an equal number of
observations. High precision measurements have small deviations from the mean. The observations of a
low precision measurement will have relatively few observations close to the mean.
Figure 1 Two normal distributions
Measured value x
Number of
observations
High precision
Low precision
Mean X
X (’X-bar’)
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