Error Propagation Arithmetic Mean
Contents |
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us propagation of error division Learn more about Stack Overflow the company Business Learn more about hiring developers
Error Propagation Physics
or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question error propagation calculator and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a error propagation average question Anybody can answer The best answers are voted up and rise to the top Error propagation on weighted mean up vote 1 down vote favorite I understand that, if errors are random and independent, the addition (or difference) of two measured quantities, say $x$ and $y$, is equal to the quadratic sum of the two errors. In other words, the error of $x + y$
Error Propagation Chemistry
is given by $\sqrt{e_1^2 + e_2^2}$, where $e_1$ and $e_2$ and the errors of $x$ and $y$, respectively. However, I have not yet been able to find how to calculate the error of both the arithmetic mean and the weighted mean of the two measured quantities. How do errors propagate in these cases? statistics error-propagation share|cite|improve this question edited Mar 22 '12 at 17:02 Michael Hardy 158k15145350 asked Mar 22 '12 at 13:46 plok 10815 add a comment| 2 Answers 2 active oldest votes up vote 3 down vote accepted The first assertion assumes one takes mean squared errors, which in probabilistic terms translates into standard deviations. Now, probability says that the variance of two independent variables is the sum of the variances. Hence, if $z = x + y$ , $\sigma_z^2 = \sigma_x^2 + \sigma_y^2 $ and $$e_z = \sigma_z = \sqrt{\sigma_x^2 + \sigma_y^2} = \sqrt{e_x^2 + e_y^2} $$ Knowing this, and knowing that $Var(a X) = a^2 Var(X)$, if $z = a x + (1-a) y$ (weighted mean, if $ 0\le a \le1$) we get: $$\sigma_z^2 = a^2\sigma_x^2 + (1-a)^2\sigma_y^2 $$ $$e_z = \sqrt{a^2 e_x^2 + (1-a)^2 e_y^2} = a \sqrt{ e_x^2 + \l
Engineering Medicine Agriculture Photosciences Humanities Periodic Table of the Elements Reference Tables error propagation square root Physical Constants Units and Conversions Organic Chemistry Glossary Search site error propagation inverse Search Search Go back to previous article Username Password Sign in Sign in Sign
Error Propagation Reciprocal
in Registration Forgot password Expand/collapse global hierarchy Home Core Analytical Chemistry Quantifying Nature Expand/collapse global location Propagation of Error Last updated 20:33, 14 May http://math.stackexchange.com/questions/123276/error-propagation-on-weighted-mean 2016 Save as PDF Share Share Share Tweet Share IntroductionDerivation of Exact FormulaDerivation of Arithmetic ExampleCaveats and WarningsDisadvantages of Propagation of Error ApproachTreatment of Covariance TermsReferencesContributors Propagation of Error (or Propagation of Uncertainty) is defined as the effects on a function by a variable's uncertainty. It is http://chem.libretexts.org/Core/Analytical_Chemistry/Quantifying_Nature/Significant_Digits/Propagation_of_Error a calculus derived statistical calculation designed to combine uncertainties from multiple variables, in order to provide an accurate measurement of uncertainty. Introduction Every measurement has an air of uncertainty about it, and not all uncertainties are equal. Therefore, the ability to properly combine uncertainties from different measurements is crucial. Uncertainty in measurement comes about in a variety of ways: instrument variability, different observers, sample differences, time of day, etc. Typically, error is given by the standard deviation (\(\sigma_x\)) of a measurement. Anytime a calculation requires more than one variable to solve, propagation of error is necessary to properly determine the uncertainty. For example, lets say we are using a UV-Vis Spectrophotometer to determine the molar absorptivity of a molecule via Beer's Law: A = ε l c. Since at least two of the variables have an uncertainty based on the equipment
equations in this document used the SYMBOL.TTF font. Not all computers and browsers supported that font, so this has been re-edited to make it more browser friendly. If any errors remain, please let me know. One of the standard notations https://www.lhup.edu/~dsimanek/errors.htm for expressing a quantity with error is x ± Δx. In some cases I find it more convenient to use upper case letters for measured quantities, and lower case for their errors: A ± a. The notation
be down. Please try the request again. Your cache administrator is webmaster. Generated Fri, 14 Oct 2016 14:51:23 GMT by s_ac15 (squid/3.5.20)