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When we measure quantities in physics, we're (implicitly) assuming that there is some underlying probability distribution from which the measured values will be drawn. Typically that distribution is peaked around some central value, and what we'd like to find out is the central value. But we can't actually know that. Given a set of measurements, maximum ...


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As you describe it, each measurement is guaranteed to be within $\pm 0.5$ mm. If you measure the same object $10$ times and are consistent, the standard deviation of the measurements will be $0$. That clearly does not reflect reality-there is no random error, but there is a systematic error that could be as large as $\pm 0.5$ mm. If you have ten ...


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The traditional least-squares fitting or chi-squared minimisation route of fitting a straight line makes the implicit assumption that the errors on the x-axis quantity are negligible. If that is so, then there is no reason why you can't use the uncertainty in the gradient as the uncertainty in $R$. I guess from your question though, that this is not the ...


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I would avoid using a spline in data analysis in general. The spline draws smooth curves through arbitrary sets of points but destroys a lot of the information in the points and adds extraneous, meaningless "information". Use it for making things pretty, not for analysis, unless you really think your data should follow a power series (which would be rather ...


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Model two consecutive measurements as the real values plus some noise. Call the first measured temperature $T_1$ and the second $T_2$. Call the measured noises $\gamma_1$ and $\gamma_2$, and suppose that they are drawn from a distribution $\Gamma(\gamma)$ and are uncorrelated. The (approximation to the) derivative is $$\text{Derivative} \approx \frac{(T_2 ...


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Your question is valid and is very good you are thinking this way so young. First, error propagation is a whole area of its own and there is not a unique way to do so, nor there is an absolute best way to be provided. So much so that the ISO document used for having a consensus on this, is called "Guide to the Expression of Uncertainty in Measurement", not ...


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I think you should have a look in this http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_Propagation_sp13.pdf it should clear up how to do error estimation in a more rigorous manner. I would only worry about the first two sections on addition and multiplication if you haven't covered calculus yet. This method of taking the maximum and minimum ...


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When proving addition of fractional uncertainties, one neglects the product of uncertainties. In your case the product of fractional uncertainties is (0.01)(0.02) = 0.0002 which is considerably less than the sum of them 0.01 + 0.02 = 0.03. This is the discrepancy you see in multiplication example. Nevertheless if you take significant figures only in your ...



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