Calculating Absolute Error
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The difference between two measurements is called a variation in the measurements. Another word for this variation - or uncertainty in measurement - is "error." This "error" is not the same as a "mistake." It does not calculating percent error mean that you got the wrong answer. The error in measurement is a mathematical way to calculating absolute error physics show the uncertainty in the measurement. It is the difference between the result of the measurement and the true value of what you absolute error formula were measuring. The precision of a measuring instrument is determined by the smallest unit to which it can measure. The precision is said to be the same as the smallest fractional or decimal division on the scale of the
Calculating Absolute Deviation
measuring instrument. Ways of Expressing Error in Measurement: 1. Greatest Possible Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. The greatest possible error when measuring is considered to be one half of that measuring unit. For example, you measure a length to be 3.4 cm. Since the measurement was made to the nearest tenth, the greatest possible error will be half of one tenth, calculating percentage error or 0.05. 2. Tolerance intervals: Error in measurement may be represented by a tolerance interval (margin of error). Machines used in manufacturing often set tolerance intervals, or ranges in which product measurements will be tolerated or accepted before they are considered flawed. To determine the tolerance interval in a measurement, add and subtract one-half of the precision of the measuring instrument to the measurement. For example, if a measurement made with a metric ruler is 5.6 cm and the ruler has a precision of 0.1 cm, then the tolerance interval in this measurement is 5.6 0.05 cm, or from 5.55 cm to 5.65 cm. Any measurements within this range are "tolerated" or perceived as correct. Accuracy is a measure of how close the result of the measurement comes to the "true", "actual", or "accepted" value. (How close is your answer to the accepted value?) Tolerance is the greatest range of variation that can be allowed. (How much error in the answer is occurring or is acceptable?) 3. Absolute Error and Relative Error: Error in measurement may be represented by the actual amount of error, or by a ratio comparing the error to the size of the measurement. The absolute error of the measurement shows how large the error actually is, while the relative error of the measurement shows how large the error is in relation to the
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Absolute Error Vs Relative Error Formula
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How Do You Find The Absolute Error
difference between the measured or inferred value of a quantity and its actual value , given by (sometimes with the absolute value taken) is called http://www.regentsprep.org/regents/math/algebra/am3/LError.htm 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 Functions with Formulas, Graphs, http://mathworld.wolfram.com/AbsoluteError.html 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 experts: dynamic textbook, lesson plans, widgets, interactiv
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 http://www.mathsisfun.com/measure/error-measurement.html instrument measures in "1"s then any value between 6½ and 7½ is measured as http://www.wikihow.com/Calculate-Relative-Error "7" When your instrument measures in "2"s then any value between 7 and 9 is measured 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 the value could be between 7 absolute error 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 is the difference between the actual calculating absolute error 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: Percentage Error = 2.63...% Example: You measure the plant to be 80 cm high (to the nea
this Article Home » Categories » Education and Communications » Subjects » Mathematics ArticleEditDiscuss Edit ArticlewikiHow to Calculate Relative Error Two Methods:Calculating Absolute ErrorCalculating Relative ErrorCommunity Q&A Absolute error is the actual amount you were off, or mistaken by, when measuring something. Relative error compares the absolute error against the size of the thing you were measuring. In order to calculate relative error, you must calculate the absolute error as well. If you tried to measure something that was 12 inches long and your measurement was off by 6 inches, the relative error would be very large. But, if you tried to measure something that was 120 feet long and only missed by 6 inches, the relative error would be much smaller -- even though the value of the absolute error, 6 inches, has not changed.[1] Steps Method 1 Calculating Absolute Error 1 When given an expected value, subtract the value you got from the expected value to get the Absolute Error. An expected value is usually found on tests and school labs. Basically, this is the most precise, common measurement to come up with, usually for common equations or reactions. You can compare your own results to get Absolute Error, which measures how far off you were from the expected results. To do so, simply subtract the measured value from the expected one. Even if the result is negative, make it positive. This is your absolute error![2] Example: You want to know how accurately you estimate distances by pacing them off. You pace from one tree to another and estimate that they're 18 feet apart. This is the experimental value. Then you come back with a long measuring tape to measure the exact distance, finding out that the trees are in fact 20 feet (6 meters) apart. That is the "real" value. Your absolute error is 20 - 18 = 2 feet (60.96 centimeters).[3] 2 Alternatively, when measuring something, assume the absolute error to be the smallest unit of measurement at your disposal. For example, if you're measuring something with a meter stick, the smallest unit marked on the meter stick is 1 millimeter (mm). So you know that your measurement is accurate to within + or - 1 mm; your absolute error