Define The Term Absolute Error. Given That
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Absolute Error Formula
developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error Analysis> History and Terminology>Disciplinary Terminology>Religious Terminology> Absolute
Absolute Error Calculator
Error The difference between the measured or inferred value of a quantity and its actual value , given by (sometimes with the absolute value
Absolute Error Definition Math
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. and Stegun, I.A. (Eds.). Handbook of Mathematical relative error definition 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 sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education
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 absolute error example Last updated: Tue Sep 27 2016 Created, developed, and nurturedbyEricWeisstein absolute error physics at WolframResearch Probability and Statistics>Error Analysis> History and Terminology>Disciplinary Terminology>Religious Terminology> Absolute Error The difference absolute error and relative error in numerical analysis between the measured or inferred value of a quantity and its actual value , given by (sometimes with the absolute value taken) is called the http://mathworld.wolfram.com/AbsoluteError.html 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. and Stegun, I.A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical http://mathworld.wolfram.com/AbsoluteError.html 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 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&raqu
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 Examples: When your instrument measures in "1"s then any value between 6½ and 7½ is measured as "7" When http://www.mathsisfun.com/measure/error-measurement.html your instrument measures in "2"s then any value between 7 and 9 is measured as "8" Plus http://user.physics.unc.edu/~deardorf/uncertainty/definitions.html 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 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 absolute error 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 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. absolute error definition 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: Percentage Error = 2.63...% Example: You measure the plant to be 80 cm high (to the nearest cm) This means you could be up to 0.5 cm wrong (the plant could be between 79.5 and 80.5 cm high) Height = 80 ±0.5 cm So: Absolute Error = 0.5 cm And: Relative Error = 0.5 cm = 0.00625 80 cm And: Percentage Error = 0.625% Area When working out areas you need to think about both the width and length ... they could both be the smallest possible measure, or both the largest. Example: Alex measured the field to the nearest meter, and got a width of 6 m and a lengt
the range of meanings. The definitions are taken from a sample of reference sources that represent the scope of the topic of error analysis. Definitions from Webster's dictionary are also included for several of the terms to show the contrast between common vernacular use and the specific meanings of these terms as they relate to scientific measurements. Sources: Taylor, John. An Introduction to Error Analysis, 2nd. ed. University Science Books: Sausalito, CA, 1997. Bevington, Phillip R. and D. Keith Robinson. Data Reduction and Error Analysis for the Physical Sciences, 2nd. ed. McGraw-Hill: New York, 1992. Baird, D.C. Experimentation: An Introduction to Measurement Theory and Experiment Design, 3rd. ed. Prentice Hall: Englewood Cliffs, NJ, 1995. ISO. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization (ISO) and the International Committee on Weights and Measures (CIPM): Switzerland, 1993. Fluke. Calibration: Philosophy and Practice, 2nd. ed. Fluke Corporation: Everett, WA, 1994. Webster's Tenth New Collegiate Dictionary, Merriam-Webster: Springfield, MA, 2000. Notes: Many of the terms below are defined in the International Vocabulary of Basic and General Terms in Metrology (abbreviated VIM), and their reference numbers are shown in brackets immediately after the term. Since the meaning and usage of these terms are not consistent among other references, alternative (and sometimes conflicting) definitions are provided with the name and page number of the reference from the above list. Comments are included in italics for clarification. References are only cited when they explicitly define a term; omission of a reference for a particular term generally indicates that the term was not used or clearly defined by that reference. Even more diverse usage of these terms may exist in other references not cited here. uncertainty (of measur