—errorless, adj. —errorlessly, adv./er"euhr/, n.1. a deviation from accuracy or correctness; a mistake, as in action or speech: His speech contained several factual errors.2. belief in something untrue; the holding of mistaken opinions.3. the condition of believing what is not true: in error about the date.4. a moral offense; wrongdoing; sin.5. Baseball. a misplay that enables a base runner to reach base safely or advance a base, or a batter to have a turn at bat prolonged, as the dropping of a ball batted in the air, the fumbling of a batted or thrown ball, or the throwing of a wild ball, but not including a passed ball or wild pitch.6. Math. the difference between the observed or approximately determined value and the true value of a quantity.7. Law.a. a mistake in a matter of fact or law in a case tried in a court of record.b. See writ of error.8. Philately. a stamp distinguished by an error or errors in design, engraving, selection of inks, or setting up of the printing apparatus. Cf. freak1 (def. 5), variety (def. 8).
* * *In applied mathematics, the difference between a value and an estimate of that value.In statistics, a common example is the difference between the mean age of a given group of people (see mean, median, and mode) and that of a sample drawn from the group. In numerical analysis, an example of round-off error is the difference between the true value of pi and commonly substituted expressions like 227 and shorter versions like 3.14159. Truncation error results from using only the first few terms of an infinite series. Relative error is the ratio of the size of an error to the size of the quantity measured, and percentage error is relative error expressed as a percent.
* * *in applied mathematics, the difference between a true value and an estimate, or approximation, of that value. In statistics, a common example is the difference between the mean of an entire population and the mean of a sample drawn from that population. In numerical analysis, round-off error is exemplified by the difference between the true value of the irrational number π and the value of rational expressions such as 22/7, 355/113, 3.14, or 3.14159. Truncation error results from ignoring all but a finite number of terms of an infinite series. For example, the exponential function ex may be expressed as the sum of the infinite series1 + x + x2/2 + x3/6 + ⋯ + xn/n! + ⋯Stopping the calculation after any finite value of n will give an approximation to the value of ex that will be in error, but this error can be made as small as desired by making n large enough.The relative error is the numerical difference divided by the true value; the percentage error is this ratio expressed as a percent. The term random error is sometimes used to distinguish the effects of inherent imprecision from so-called systematic error, which may originate in faulty assumptions or procedures. The methods of mathematical statistics are particularly suited to the estimation and management of random errors.
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