Error Propagation For Average
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Community Forums > Mathematics > Set Theory, Logic, Probability, Statistics > Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! Everyone who loves science is here! Error propagation with averages and standard deviation Page 1 of 2 1 propagation of error mean 2 Next > May 25, 2012 #1 rano I was wondering if someone could please help propagation of error calculator me understand a simple problem of error propagation going from multiple measurements with errors to an average incorporating these errors. I have looked on several error propagation average standard deviation error propagation webpages (e.g. UC physics or UMaryland physics) but have yet to find exactly what I am looking for. I would like to illustrate my question with some example data. Suppose we want to know the mean ± standard deviation how to find error propagation (mean ± SD) of the mass of 3 rocks. We weigh these rocks on a balance and get: Rock 1: 50 g Rock 2: 10 g Rock 3: 5 g So we would say that the mean ± SD of these rocks is: 21.6 ± 24.6 g. But now let's say we weigh each rock 3 times each and now there is some error associated with the mass of each rock. Let's say that the mean ± SD of each rock mass
Error Propagation Example
is now: Rock 1: 50 ± 2 g Rock 2: 10 ± 1 g Rock 3: 5 ± 1 g How would we describe the mean ± SD of the three rocks now that there is some uncertainty in their masses? Would it still be 21.6 ± 24.6 g? Some error propagation websites suggest that it would be the square root of the sum of the absolute errors squared, divided by N (N=3 here). But in this case the mean ± SD would only be 21.6 ± 2.45 g, which is clearly too low. I think this should be a simple problem to analyze, but I have yet to find a clear description of the appropriate equations to use. If my question is not clear please let me know. Any insight would be very appreciated. rano, May 25, 2012 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength May 25, 2012 #2 viraltux rano said: ↑ I was wondering if someone could please help me understand a simple problem of error propagation going from multiple measurements with errors to an average incorporating these errors. I have looked on several error propagation webpages (e.g. UC physics or UMaryland physics) but have yet to find exactly what I am looking for. I think this should be a simple
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and policies of this site About Us Learn more about Stack Overflow error propagation physics the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges error propagation calculus Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only https://www.physicsforums.com/threads/error-propagation-with-averages-and-standard-deviation.608932/ takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Average over two variables: Why do standard error of mean and error propagation differ and what does that mean? up vote 3 down vote favorite I'm doing an experiment with a cryostat to http://stats.stackexchange.com/questions/71419/average-over-two-variables-why-do-standard-error-of-mean-and-error-propagation determine the critical temperature for lead. To avoid asymmetries, I determine the critical temperature both through heating (going from 2 K to 10 K) and cooling (10 K -> 2 K). Now I have two values, that differ slighty and I average them. So a measurement of (6.942 $\pm$ 0.020) K and (6.959 $\pm$ 0.019) K gives me an average of 6.951 K. Now the question is: what is the error of that average? One way to do it would be to calculate the variance of this sample (containing two points), take the square root and divide by $\sqrt{2}$. This gives me an SEM of 0.0085 K, which is too low for my opinion (where does this precision come from?) The other way is to say the the mean is a function of two variables, $\bar{T} = \frac{T_1 + T_2}{2}$, therefore by error propagation the error is $\Delta T = \frac12\sqrt{(\Delta T_1)^2+(\Delta T_2)^2}$, and that gives me a much more rational value of 0.014. I see how those values differ in terms of numbers, but which one is correct when talking abou
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