Mathematics Absolute Error
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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: Wed Oct 19 absolute error calculator 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Error Analysis>
Absolute Error Formula
History and Terminology>Disciplinary Terminology>Religious Terminology> Absolute Error The difference between the measured or inferred value of a
Relative Error Definition
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 difference
Absolute Error Definition
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 THIS relative error formula 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 39th prime (complement S) intersect (A union B)
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 what is absolute error measure Examples: When your instrument measures in "1"s then any value between 6½ and absolute error formula physics 7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is measured absolute error formula chemistry as "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 http://mathworld.wolfram.com/AbsoluteError.html 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 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 https://www.mathsisfun.com/measure/error-measurement.html 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. 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°
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the difference between an estimated or measured value and it's actually value. To find out the absolute error you would have to measurement or estimate of whatever values. At which point you would like to take the difference between the approximated value and the original value. Absolute Error formula = Original number - Approximated number
How to find Absolute Error Back to Top For example an approximation, we discover that the approximated value may be more or less than the original number. The difference between two values is called as the absolute error. An approximation of a correct value x, we define the absolute value of the difference between the two more. Solved Examples Question1: The number of peoples are in a meeting is 730. Find the absolute error Solution: Number of peoples= 730Number of peoples correct to nearest hundred = 700Formula = Original number - Approximated numberTherefore,Absolute Error = 730 - 700 = 30The solution is 30. Question2: The number of children are in an orphan is 820. Find the absolute error Solution: Number of children = 820Number of children correct to nearest hundred = 800Formula = Original number - Approximated numberAbsolute Error = 820 - 800 = 20Therefore absolute error is 20 Question3: 21.571 is the True value, 20.000 is the Recorded Value. Find the absolute error? Solution: Formula = (True value) - (Recorded Value)Absolute error = 21.571 - 20.000 = 1.571Therefore absolute error = 1.571 Question4: What is the absolute error for 56 - 0.70? Solution: Formula = Original number - Approximated numberAbsolute error = 56 - 0.70 = 55.3Therefore,Absolute error = 55.3 Question5: How do you solve this absolute error problem? Robert measured the weight of a pineapple approximated as 682.325 grams, but the original weight is 684.075 Solution: Formula = Original number - App