Error Propagation Calculator Mean
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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 error propagation calculator excel science is here! Error propagation with averages and standard deviation Page 1 of error propagation calculator physics 2 1 2 Next > May 25, 2012 #1 rano I was wondering if someone could please help me understand
Error Propagation Formula Calculator
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
How Do You Calculate Error Propagation
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 (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 error propagation mean value 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 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 o
or more quantities, each with their individual uncertainties, and then combine the information from these quantities in order to come up with a final result of our experiment. How can you state your answer for the combined result of these measurements and their uncertainties scientifically? The answer to this fairly common question depends on how the individual
Error Propagation Example
measurements are combined in the result. We will treat each case separately: Addition of measured quantities If error propagation formula derivation you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final result, R, is the sum or difference error propagation rules of these quantities, then the uncertainty dR is: Here the upper equation is an approximation that can also serve as an upper bound for the error. Please note that the rule is the same for addition and subtraction of quantities. Example: Suppose we https://www.physicsforums.com/threads/error-propagation-with-averages-and-standard-deviation.608932/ have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Then the displacement is: Dx = x2-x1 = 14.4 m - 9.3 m = 5.1 m and the error in the displacement is: (0.22 + 0.32)1/2 m = 0.36 m Multiplication of measured quantities In the same way as for sums and differences, we can also state the result for the case of multiplication and division: Again the upper line is an approximation and the lower line is the http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm exact result for independent random uncertainties in the individual variables. And again please note that for the purpose of error calculation there is no difference between multiplication and division. Example: We have measured a displacement of x = 5.1+-0.4 m during a time of t = 0.4+-0.1 s. What is the average velocity and the error in the average velocity? v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = 12.75 m/s [(0.4/5.1)2 + (0.1/0.4)2]1/2 = 3.34 m/s Multiplication with a constant What if you have measured the uncertainty in an observable X, and you need to multiply it with a constant that is known exactly? What is the error then? This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the above rule for multiplication of two quantities, you see that this is just the special case of that rule for the uncertainty in c, dc = 0. Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 m/s, how long has it been in free fall? Answer: we can calculate the time as (g = 9.81 m/s2 is assumed to be known exactly) t = - v / g = 3.8 m/s / 9.81 m/s2 = 0.38
known or estimated uncertainties. The calculations may involve algebraic operations http://web.mst.edu/~gbert/JAVA/uncertainty.HTML such as: Z = X + Y ; Z = X - Y ; Z = X x Y ; Z = X/Y ; Z = XY or mathematical functions of the type: Z = 1/X ; Z = ln(X) ; Z = log10(X) ; Z = 10X error propagation ; Z = eX ; Z = sqrt(X) . If uncertainties (dX, dY) are provided for the input quantities (X,Y), the program will perform the operation or function to calculate the answer (Z) and will also calculate the uncertainty in the answer (dZ). The program will assume the value has no error propagation calculator uncertainty if an uncertainty is not provided. Operation: Position the cursor on the blank under "X", click the mouse, and type a value. Alternately, press the TAB key until the cursor appears in this blank, then type the number. In case of an error, use normal text-editing procedures. Enter values for X and dX, and possibly for Y and dY. (The TAB key moves the cursor through the blanks in the order: X, dX, Y, dY). Click on the button for the desired operation or function. The equation for the calculation appears in the central blank, and the values of Z and dZ appear in their respective blanks. There are buttons for transferring values from Z to a MEMory location, or to the blanks for X or Y; or from the MEMory to X or Y. top