Probable Percent Error
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Can Percent Error Be Negative
Glossary Kepler's Third Law Significant Figures Percent Error Formula Small-Angle Formula Stellar Parallax Finder Chart Iowa Robotic Telescope Sidebar[Skip] Glossary Index Kepler's Third LawSignificant FiguresPercent Error FormulaSmall-Angle FormulaStellar ParallaxFinder Chart Percent Error Formula When you calculate results that are aiming for known values, the percent error formula is useful tool for determining the precision of your calculations. The formula is given by: The negative percent error experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good. It is always necessary to understand the cause of the error, such as whether it is due to the imprecision of your equipment, your own estimations, or a mistake in your experiment.Example: The 17th century Danish astronomer, Ole Rømer, observed that the periods of the satellites of Jupiter would appear to fluctuate depending on the distance of Jupiter from Earth. The further away Jupiter was, the longer the satellites would take to appear from behind the planet. In 1676, he determined that this phenomenon was due to the fact that the speed of light was finite, and subsequently estimated its velocity to be approximately 220,000 km/s. The current accepted value of the speed of light is almost 299,800 km/s. What was the percent error of Rømer's estimate?Solution:experimental value = 220,000 km/s = 2.2 x 108 m/stheoretical value = 299,800 km/s 2.998 x 108 m/s So Rømer was quite a bit off by our standards today, but
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 a good percent error measure Examples: When your instrument measures in "1"s then any value between 6½
Percent Error Worksheet
and 7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is
Percent Error Definition
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 http://astro.physics.uiowa.edu/ITU/glossary/percent-error-formula/ 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 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 https://www.mathsisfun.com/measure/error-measurement.html 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. 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 =
will lie within the interval and half outside.[1] Thus https://en.wikipedia.org/wiki/Probable_error it is equivalent to half the interquartile range, or http://www.regentsprep.org/regents/math/algebra/am3/LErrorD.htm the median absolute deviation. The probable error can also be expressed as a multiple of the standard deviation σ,[1][2] γ = 0.6745 × σ {\displaystyle \gamma =0.6745\times \sigma } (where the multiplying factor 0.6745 derives from percent error the normal distribution), which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. One use of the term probable error in statistics is as the name for the scale parameter of the Cauchy distribution. See also[edit] probable percent error Circular error probable References[edit] ^ a b Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9 ^ Zwillinger, D.; Kokosa, S. (2000) CRC Standard Probability and Statistics Tables and Formulae, Chapman & Hall/CRC. ISBN 1584880597 (Section 2.2.13) Retrieved from "https://en.wikipedia.org/w/index.php?title=Probable_error&oldid=732727418" Categories: Theory of probability distributionsErrorMeasurementUncertainty of numbers Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaWikipedia store Interaction HelpAbout WikipediaCommunity portalRecent changesContact page Tools What links hereRelated changesUpload fileSpecial pagesPermanent linkPage informationWikidata itemCite this page Print/export Create a bookDownload as PDFPrintable version Languages Add links This page was last modified on 2 August 2016, at 21:05. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this
5 inches, when the real length is 6 inches. Notice how the percentage of error increases as the student uses this measurement to compute surface area and volume. Measurement Compute Surface Area Compute Volume The side of a cube is measured. Measurement: 5 in. Actual size: 6 in. Percent of error = Surface area computed with measurement: SA = 25 • 6 = 150 sq. in. Actual surface area: SA = 36 • 6 = 216 sq. in. Percent of error = Volume computed with measurement: V = 5 ³ = 125 cubic in.Actual volume: V = 6 ³ = 216 cubic in. Percent of error = rounded to nearest tenth. 2. A box has the measurements 1.4 cm by 8.2 cm by 12.5 cm. Find the percent of error in calculating its volume. ANSWER: Since no other values are given, we will use the greatest possible error based upon the fact that these measurements were taken to the nearest tenth of a centimeter, which will be 0.05 cm. Volume as measured: 1.4 x 8.2 x 12.5 = 143.5 cubic cm Maximum volume (+0.05) : 1.45 x 8.25 x 12.55 = 150.129375 cubic cm Minimum volume (-0.05): 1.35 x 8.15 x 12.45 = 136.981125 cubic cm Possible error in volume: Maximum - measured = 6.629375 cubic cm Measured - minimum = 6.518875 cubic cm Use the "greatest" possible error in volume: 6.629375 cubic cm Remember that percent of error is the relative error times 100%. The percent of error is approximately 5%. Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts