Absolute Error Problems
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of Accuracy Accuracy depends on the instrument you are measuring with. But as a general rule: The degree of accuracy is half a unit each side of the unit of measure absolute error formula Examples: When your instrument measures in "1"s then any value between 6½ and
Absolute Error Calculator
7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is measured as
Absolute Error Example
"8" Plus or Minus We can show the error using the "Plus or Minus" sign: ± When the value could be between 6½ and 7½ 7 ±0.5 The error is ±0.5 When the
How To Find Absolute Error
value could be between 7 and 9 8 ±1 The error is ±1 Example: a fence is measured as 12.5 meters long, accurate to 0.1 of a meter Accurate to 0.1 m means it could be up to 0.05 m either way: Length = 12.5 ±0.05 m So it could really be anywhere between 12.45 m and 12.55 m long. Absolute, Relative and Percentage Error The absolute error physics Absolute Error is the difference between the actual and measured value But ... when measuring we don't know the actual value! So we use the maximum possible error. In the example above the Absolute Error is 0.05 m What happened to the ± ... ? Well, we just want the size (the absolute value) of the difference. The Relative Error is the Absolute Error divided by the actual measurement. We don't know the actual measurement, so the best we can do is use the measured value: Relative Error = Absolute Error Measured Value The Percentage Error is the Relative Error shown as a percentage (see Percentage Error). Let us see them in an example: Example: fence (continued) Length = 12.5 ±0.05 m So: Absolute Error = 0.05 m And: Relative Error = 0.05 m = 0.004 12.5 m And: Percentage Error = 0.4% More examples: Example: The thermometer measures to the nearest 2 degrees. The temperature was measured as 38° C The temperature could be up to 1° either side of 38° (i.e. between 37° and 39°) Temperature = 38 ±1° So: Absolute Error = 1° And: Relative Error = 1° = 0.0263... 38° And:
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book can absolute error be negative Wolfram Web Resources» 13,594 entries Last updated: Tue Sep 27 mean absolute error 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error Analysis> History and Terminology>Disciplinary absolute percent error Terminology>Religious Terminology> Absolute Error The difference between the measured or inferred value of a quantity and its actual value , given by (sometimes http://www.mathsisfun.com/measure/error-measurement.html with the absolute value taken) is called the absolute error. The absolute error of the sum or difference of a number of quantities is less than or equal to the sum of their absolute errors. SEE ALSO: Error Propagation, Percentage Error, Relative Error REFERENCES: Abramowitz, M. http://mathworld.wolfram.com/AbsoluteError.html and Stegun, I.A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p.14, 1972. Referenced on Wolfram|Alpha: Absolute Error CITE THIS AS: Weisstein, Eric W. "Absolute Error." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbsoluteError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study
and Relative Error 1.3 Significant Digits 2 Numeric Representation 3 Iteration 4 Linear Algebra 5 Interpolation 6 Least Squares 7 Taylor Series 8 Bracketing 9 The Five Techniques 10 Root Finding 11 Optimization 12 Differentiation 13 Integration 14 Initial-value https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/01Error/Error/ Problems 15 Boundary-value Problems Appendices 1.2 Absolute and Relative Error Introduction Theory HOWTO Examples Questions Matlab Maple Introduction There are two techniques for measuring error: the absolute error of an approximation and the relative error of the approximation. The first gives how large the error is, while the second gives how large the error is relative to the correct value. Background None. References Bradie, Section 1.3, Roundoff Error, p.34. Mathews, Section 1.3, Error Analysis, p.24. Weisstein, http://mathworld.wolfram.com/AbsoluteError.html. Weisstein, absolute error http://mathworld.wolfram.com/RelativeError.html. Theory Absolute Error Given an approximation a of a correct value x, we define the absolute value of the difference between the two values to be the absolute error. We will represent the absolute error by Eabs, therefore It is often sufficient to record only two decimal digits of the absolute error. Thus, it is sufficient to state that the absolute error of the approximation 3.55 to the correct value 3.538385 is 0.012. There absolute error problems are two problems with using the absolute error: Significance It gives you a feeling of the size of the error but how significant is the error? If the absolute error was 3.52, is this significant? If the correct value is x = 5030235.23, then probably not, however if the correct value is x = 5.03023523, then an absolute error 3.52 is probably very significant. Units The absolute error will change depending on the units used. The absolute error of the approximation 2.4 MV of an actual voltage of 2.573243 MV is 0.17 MV, whereas the absolute error of the approximation 2400000 V to an actual voltage of 2573243 V is 170000 V. Relative Error To solve the problems of significance and units, we may compare the absolute error relative to the correct value. Thus, we define the relative error to be the ratio between the absolute error and the absolute value of the correct value and denote it by Erel: In this equation, any units cancel, so the relative errors of the approximations 2.4 MV and 2400000 V versus the actual voltages of 2.573243 MV and 2573243 V, respectively, are equal. Also, a relative error of 0.01 means that the approximation is correct to within one part in one hundred, regardless of the size of the actual value. Whether this is sufficiently accurate depends on the requirements. In t