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If the times N of measurement are labelled as x 1 , x 2 , x 3 ,…, x n , the true value is a , then:
(1)Arithmetic mean value:
It can be proved that the arithmetic mean value is the best approximation of the true value of the observed object without systematic error. When n →∞ , a ≈ x .
(2) Mean absolute error of arithmetic mean value:
(3) Standard deviation of measurement column:
(4) Standard deviation of arithmetic mean value:
(1) In general, the instrument error indicated in the specification of the instrument can be viewed as the error of a single measurement.
(2) If the instrument error is not given, for an instrument with an estimation of reading, half of the minimum scale of the instrument as the error
ε
of a single measurement, and
of that also functions as the standard deviation
S
of the measurement.
(3) For some instruments without an estimation of reading,
of the smallest scale as the error of a single measurement is available.