1.2 Estimation of Measuring Error

1.2.1 Multiple equal precision measurement

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:

1.2.2 Error of single measurement

(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. kwjzXNs0a7pXtGcPgtpeKDRlHeEOKQrESP113qAvLEzUPl2FinfljB0Z6kNjhWT6