Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or

approximations are used instead of the real data (e.g., 3.14 instead of π).

In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.

Formal Definition

One commonly distinguishes between the relative error and the absolute error.

Given some value v and its approximation v_approx, the absolute error is

where the vertical bars denote the absolute value. If $v \ne 0,$ the relative error is

and the percent error is

In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percent error is the relative error expressed in terms of per 100.

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Error (baseball)

In baseball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows an at bat to continue after the batter should have been put out.

The term error can also refer to the play during which an error was committed.

Relationship to other statistical categories

An error does not count as a hit but still counts as an at bat for the batter unless, in the scorer's judgment, the batter would have reached first base safely but one or more of the additional base(s) reached was the result of the fielder's mistake. In that case, the play will be scored both as a hit (for the number of bases the fielders should have limited the batter to) and an error. However, if a batter is judged to have reached base solely because of a fielder's mistake, it is scored as a "hit on error," and treated the same as if a batter was put out, hence lowering his batting average.