Absolute Error Mathworld
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep what is relative error 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error relative error definition Analysis> History and Terminology>Disciplinary Terminology>Religious Terminology> Absolute Error The difference between the measured or inferred value of
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a quantity and its actual value , given by (sometimes with the absolute value taken) is called the absolute error. The absolute error of the sum or
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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. 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 relative error formula 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 sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Language» Knowledge-based programming for everyone. Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: normal distribution bet3 < aleph3 Champernowne constant
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram
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Web Resources» 13,594 entries Last updated: Tue Sep 27 absolute error and percent error 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error Analysis> Percentage Error The percentage can absolute error be negative error is 100% times the relative error. SEE ALSO: Absolute Error, Error Propagation, Percent, Relative Error REFERENCES: Abramowitz, M. and Stegun, I.A. (Eds.). http://mathworld.wolfram.com/AbsoluteError.html Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p.14, 1972. Referenced on Wolfram|Alpha: Percentage Error CITE THIS AS: Weisstein, Eric W. "Percentage Error." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PercentageError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and http://mathworld.wolfram.com/PercentageError.html 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 sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Language» Knowledge-based programming for everyone. Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: 5^5^5 f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2 integral representation erfc(z)
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 https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/01Error/Error/ 12 Differentiation 13 Integration 14 Initial-value Problems 15 Boundary-value Problems Appendices 1.2 Absolute and http://www.wikihow.com/Calculate-Absolute-Error 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 absolute error 1.3, Roundoff Error, p.34. Mathews, Section 1.3, Error Analysis, p.24. Weisstein, http://mathworld.wolfram.com/AbsoluteError.html. Weisstein, 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 absolute error mathworld to state that the absolute error of the approximation 3.55 to the correct value 3.538385 is 0.012. There 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
this Article Home » Categories » Education and Communications » Subjects » Mathematics » Algebra ArticleEditDiscuss Edit ArticleHow to Calculate Absolute Error Three Methods:Using the Actual Value and Measured ValueUsing the Actual Value and Relative ErrorUsing the Maximum Possible ErrorCommunity Q&A Absolute error is the difference between the measured value and the actual value.[1] It is one way to consider error when measuring the accuracy of values. If you know the actual and measured values, calculating the absolute error is a simple matter of subtraction. Sometimes, however, you may be missing the actual value, in which case you should use the maximum possible error as the absolute error.[2] If you know the actual value and the relative error, you can work backwards to find the absolute error. Steps Method 1 Using the Actual Value and Measured Value 1 Set up the formula for calculating the absolute error. The formula is Δx=x0−x{\displaystyle \Delta x=x_{0}-x}, where Δx{\displaystyle \Delta x} equals the absolute error (the difference, or change, in the measured and actual value), x0{\displaystyle x_{0}} equals the measured value, and x{\displaystyle x} equals the actual value.[3] 2 Plug the actual value into the formula. The actual value should be given to you. If not, use a standardly accepted value. Substitute this value for x{\displaystyle x}. For example, you might be measuring the length of a football field. You know that the actual, or accepted length of a professional American football field is 360 feet. So, you would use 360 as the actual value:Δx=x0−360{\displaystyle \Delta x=x_{0}-360}. 3 Find the measured value. This will be given to you, or you should make the measurement yourself. Substitute this value for x0{\displaystyle x_{0}}. For example, if you measure the football field and find that it is 357 feet long, you would use 357 as the measured value:Δx=357−360{\displaystyle \Delta x=357-360}. 4 Subtract the actual value from the measured value. Since absolute error is always positiv