Overall Error Of Measurement
Contents |
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:
Relative Error
When your instrument measures in "1"s then any value between 6½ and 7½ absolute error formula is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is measured as "8"
Relative Error Formula
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 absolute error example 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 Percentage Error The Absolute Error absolute error calculator 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 = 1° = 0.0263... 38° And: Percentage Error = 2.63...
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 Learn more about Stack Overflow the company
Relative Error Calculator
Business Learn more about hiring developers or posting ads with us Physics Questions Tags Users types of errors in measurement Badges Unanswered Ask Question _ Physics Stack Exchange is a question and answer site for active researchers, academics and students of
How To Find Absolute Error
physics. Join them; it only 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 How to combine https://www.mathsisfun.com/measure/error-measurement.html measurement error with statistic error up vote 10 down vote favorite 4 We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction time. If I now measure, say 40, 41 and 39 seconds in three runs, I will also have standard deviation of http://physics.stackexchange.com/questions/23441/how-to-combine-measurement-error-with-statistic-error 1. What is the total error then? Do I add them up, like so? $$\sqrt{1^2 + 0.1^2}$$ Or is it just the 1 and I discard the (systematic?) error of my reaction time? I wonder if I measure a huge number of times, the standard deviation should become tiny compared to my reaction time. Is the lower bound 0 or is it my reaction time with 0.1? measurement statistics error-analysis share|cite|improve this question edited Apr 9 '12 at 16:17 Qmechanic♦ 64.4k991242 asked Apr 9 '12 at 12:41 Martin Ueding 3,31221439 add a comment| 3 Answers 3 active oldest votes up vote 6 down vote accepted I think you're exercising an incorrect picture of statistics here - mixing the inputs and outputs. You are recording the result of a measurement, and the spread of these measurement values (we'll say they're normally distributed) is theoretically a consequence of all of the variation from all different sources. That is, every time you do it, the length of the string might be a little different, the air temperature might be a little different. Of course, all of these are fairly small and I'm just listing them for the sake of argument. The point is that the ultimate standard deviation of the measured value $\sigma$ should be the result
Community Forums > Physics > General Physics > We've just passed 300 Insights! View them here! What a resource! Dismiss Notice Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! Everyone who loves science is here! Total error in a measurement. Sep 8, 2008 https://www.physicsforums.com/threads/total-error-in-a-measurement.254605/ #1 Topher925 I have a question that has been bugging me lately. How is it that you determine the total error of a measurement? For example, if we are trying to measure the flow rate of water coming out of a hose. We let the water flowing through the hose fill a graduated cylinder and measure the time it takes to do it. So we would have: Flow rate = Volume / Time However lets say that we need to know the error of this measurement. Would we absolute error say that the total error is: Error = Ev*dQ/dv + Et*dQ/dt (d's are partial derivatives) Where, Q = function for flow rate Ev = max error from volume measurement Et = max error of time measurement Error = total error So the formula would ultimately be: Error = Et*-V/t^2 + Ev*1/t Would this be correct? Haven't done this in a while and its just not making sense to me? Last edited: Sep 8, 2008 Topher925, Sep 8, 2008 Phys.org - latest science and technology news stories on Phys.org overall error of •Unusual quantum liquid on crystal surface could inspire future electronics •When quantum scale affects the way atoms emit and absorb particles of light •Nanoantenna lighting-rod effect produces fast optical switches Sep 8, 2008 #2 gmax137 I think you take the *partial* derivatives of the function wrt each variable, and multiply each pd by the error, then sum them up. So in your example where F = V/t you have err = ev d(V/t)/dV + et d(V/t)/dt (where these d's are partials) You have to be careful to keep track of the units, sometimes errors are given as percent of scale and sometimes in absolute units. gmax137, Sep 8, 2008 Sep 8, 2008 #3 Topher925 gmax137 said: ↑ I think you take the *partial* derivatives of the function wrt each variable, and multiply each pd by the error, then sum them up. Thanks for the reply. Thats what I meant to say, I should probably correct that. I always get confused about this formula for some reason it just doesn't make much "physical" sense to me. Topher925, Sep 8, 2008 Sep 8, 2008 #4 gmax137 The physical meaning is this - the partial derivative of f(x,y) wrt x is how much f changes for a given change in x. Now consider ex, the error in x, as that "given change in x". Then the change in f for the change in x is ex times partial of f wrt x. gmax137, Sep 8, 2008 Sep 8, 2008 #5 Andy Resnick Science Advisor Education Advisor Insights Author Topher925 said: ↑ I hav