How to find the accuracy of approximate value

How to find the accuracy of approximate value

The quantitative concept "accuracy" of science does not exist. This qualitative concept. At protection of theses speak only about an error (for example, measurements). And even if the word "accuracy" sounded, then it must be kept in mind very indistinct measure of size, the return error.


1. Small analysis of the concept "approximate value". It is possible that the approximate result of calculation means. The error (accuracy) is set here by the performer of work. This error is specified in tables, for example "up to 10 in minus of the fourth degree". If an error relative – that as a percentage or percent shares. If calculations were conducted on the basis of a numerical row (most often Taylor) – on the basis of the module of the residual member of a row.

2. About approximate values of sizes often speak as about their estimated values. Results of measurements are accidental. Therefore it is the same random variables having the characteristics of dispersion of values as the same dispersion or page to. lake (average square deviation). In mathematical statistics the whole sections are devoted to questions of estimates of parameters. At the same time distinguish dot and interval estimates. The last are not considered here. Dot assessment of some parameter λ, subject to definition we will agree to designate λ*. Estimates of parameters are just calculated on some formulas (statisticians) meeting the requirements, the called criteria of quality of assessment.

3. The first criterion is called not shift. The fact that the average value (expected value) of assessment λ* is equal to its true value, that is M [λ *]=λ means. You should not tell criterion of quality about the others so far. Sometimes also neglect them, proving a question by the fact that the most important that assessment rather "poorly" differed from the truth. Therefore the main characteristic of dispersion – dispersion of assessment undertakes and it is just calculated. If the researcher makes the independent decision that she is rather small, then and are limited to it.

4. The average value (expected value) is most often estimated. This selective average calculated as an arithmetic average of the available results of observations of mx *= (1/n) (x1+x2 + … +xn). It is easy to show that M [mx *] =mx, that is mx * assessment which is not displaced. Find dispersion of assessment of expected value following the calculations provided on figure 1a. As the true Dx value is inaccessible, in exchange take average selective dispersion (see fig. 1b).

Author: «MirrorInfo» Dream Team