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Experimental standard deviation
For a series of n measurements of the same measurand, the quantity characterizing the dispersion
of the results and given by the formula:
being the result of the measurement and being the arithmetic mean of the n results considered.
Notes:
a. Considering the series of n values as a sample of a distribution, is an unbiased estimate of
the mean , and is an unbiased estimate of the variance , of that distribution.
b. The expression is an estimate of the standard deviation of the distribution of and
is called the experimental standard deviation of the mean.
c. “Experimental standard deviation of the mean” is sometimes incorrectly called standard error
of the mean.
Uncertainty (of measurement)
Parameter, associated with the result of a measurement that characterizes the dispersion of the values
that could reasonably be attributed to the measurand.
Notes:
a. The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width
of an interval having a stated level of confidence.
b. Uncertainty of measurement com prises, in general, m any components. Some of these components
may be evaluated from the statistical distribution of the results of series of measurements and
can be characterized by experimental standard deviations. The other components, which can
also be characterized by standard deviations, are evaluated from assumed probability distributions
based on experience or other information.
c. It is understood that the result of the measurement is the best estimate of the value of the measurand,
and that all components of uncertainty, including those arising from systematic effects, such
components associated with corrections and reference standards, contribute to the dispersion.
Error (of measurement)
Result of a measurement minus a true value of the measurand.
Notes:
a. Since a true value cannot be determined, in practice a conventional true value is used.
b. When it is necessary to distinguish “error” from “relative error,” the former is sometimes called
absolute error of measurement. This should not be confused with absolute value of error, which
is the modulus of the error.
Relative error
Error of measurement divided by a true value of the measurand.
Note:
a. Since a true value cannot be determined, in practice a conventional true value is used.
Random error
Result of a measurement minus the mean that would result from an infinite number of measurements
of the same measurand carried out under repeatability conditions.
Notes:
a. Random error is equal to error minus systematic error.
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