How to define an absolute error of measurement

How to define an absolute error of measurement

Calculation of errors of measurement is the final stage of calculations. It allows to reveal degree of a deviation of the received value from true. There are several types of such deviations, but sometimes it is enough to define only an absolute error of measurement.


1. To define an absolute error of measurement, it is necessary to find deviation size from the valid value. She says in the same units, as estimated, and equals the arithmetic difference between true and estimated values: ∆ = x1 – x0.

2. The absolute error is often used in record of some constants which are of infinitesimal or infinitely great importance. It concerns many physical and chemical constants, for example, Boltzmann's constant is equal to 1,380 6488×10^ (−23) ± 0,000 0013×10^(−23) to J / To where the value of an absolute error separates from true with the help sign ±.

3. Within mathematical statistics the measurements are performed as a result of a series of experiments which result is some sample of values. The analysis of this sample leans on methods of probability theory and assumes creation of probabilistic model. In this case the mean square deviation is accepted to an absolute error of measurement.

4. For calculation of a mean square deviation it is necessary to define average or arithmetic where xi are sample units, n is its volume; hvzv = ∑pi•xi/∑ pi is the average weighed.

5. As you can see, in the second case are considered the weight of the pi elements which show with what probability the measured size will accept any given value of a sample unit.

6. The classical formula of a mean square deviation looks as follows: σ = √ (∑ (xi – hsr)² / (n - 1)).

7. There is a concept of a relative error which is in direct dependence on absolute. It is equal to the relation of an absolute error to a calculated or valid value of size which choice depends on requirements of a specific objective.

Author: «MirrorInfo» Dream Team