# Tagged Questions

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### How should I quote errors when measurements are asymetrically clustered?

Suppose five people measure the length of a stick and report the following values 4.90cm 4.92cm 4.93cm 4.94cm 4.94cm In high school science we are told that in ...
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### Combining ±% with ±dB in measurement uncertainty

Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the ...
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### Significant figures in measurement with error

Someone can explain me what's the rule behind the correct expression of a quantity $K$ with its error $\Delta K$ as $K \pm \Delta K$? They must have the same number of significant figures? Or the ...
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### What can I say about compatibility between predictions and results?

If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\ \omega_{b_1} = 0.0707 \pm ...
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### Small question about accuracy and precision

Let's say I have a law like this, $$D=\frac{c}{r}$$ where $c$ is a constant, $r$ a distance in meter. my measures of $r$ are [$0.02m$, $0.01m$], then $<r>=0.015m$ and $\delta r = \pm 0.005m$. So ...
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### Could one measure a stick to an arbitrary precision by having its length estimated by enough people?

I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of ...
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### Measuring a fluctuating quantity: Instrument error vs. uncertainty, or both?

Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy ...
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### Error analysis and how values in references are determined

Question 1:Most science textbooks have appendixes that have a value for some physical property of some object. This includes diameter of electrons, viscosity of fluids, boiling points, etc. My ...
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### Addition according to significant digits

I have been studying about significant digits and addition rules and I can't quite digest the rules of addition completely. It states that in the answer number of decimal places will be equal to the ...
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### Significant figures vs. absolute error

On NIST Avogadro's Number, $N_A = 6.022\;141\;29 \times 10^{23} \text{ mol}^{-1}$ has 9 significant figures and a standard uncertainty of $0.000\;000\;27 \times 10^{23} \text{ mol}^{-1}$. First, can ...
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### Accuracy and Error of Atomic Clocks

I'm quoting a passage from my notes: The development of clocks based on atomic oscillations allowed measures of timing with accuracy on the order of $1$ part in $10^{14}$, corresponding to errors ...
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### How to estimate a final error when you have N experiments with N errors? [duplicate]

if we have Xo±e1, X1±e2, X2±e3, ..., Xn±en when we know these, what is going to be our estimation for X, and it's error? for example if we have 344±1, 350±2, 345±5, 338 ± 2 estimation? error of ...
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### Physics Standard Deviation

I am a physics enthusiast and I have a question: Why is it meaningless to express the '$\pm$' (standard deviation) value as a percentage?
$$x = (\overline{x}-K)\pm \Delta x\tag{1}$$ $$\Delta x = s_{\overline{x}} = \sqrt{\frac t {\sqrt n} s_x} \tag{2}$$ $$s_x = \sqrt{\frac 1 {n-1} \sum^{n}_{i=1}(x_i-\overline{x})} \tag{3}$$ $$\frac ... 1answer 81 views ### How many measurements should be done? [closed] I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard deviation? 1answer 133 views ### Measurement uncertainty of the quantity, that is function of two others quantities I'm trying to compute uncertainty for the density of the ball. I measured its radius 6 times, so I was able to compute the stastistical uncertainty (we call it uncertainty type A, I don't know, if ... 2answers 148 views ### Asymmetric uncertainties Inspired by these two question on tex.SX Asymmetrical tolerancing Asymmetric uncertainties with siunitx package I'd like to ask for a nice explanation for these kind of uncertainties, like ... 1answer 119 views ### Is this the correct way to I combine multiple interdependant pressure readings? I want to measure the density in different layers of a suspension. To do this I want to place pressure sensors at different heights. Let's assume that the sensors are not by orders of magnitude more ... 1answer 100 views ### Multimeter has a resistance If a multimeter has a resistance (1M ohm, say) when measuring voltages how do I take that into account in my error? 0answers 2k views ### How to calculate uncertainties of a natural exponential function? (I apologize if this should be posted in mathematics, however I chose to post it here as it's technically about physics) I conducted an experiment in which position of items were shifted on an ... 0answers 229 views ### How do I do error calculus right using gnuplot as an example? Given is a set of measurements with their respective errors for example an energy spectrum. In gnuplot one is to fit a function  f(x;\{p_i\}) depending on a variable x and on fit parameters p_i. ... 3answers 362 views ### Significant Figures [closed] Subtract 0.2 J from 7.26 J. Express your answer to the correct number of significant figures for the given data. I think its 7, but the answer is 7.1. HOW? 1answer 2k views ### Calculating the Uncertainty for an Average Value [closed] How would I calculate the uncertainty for the average of this set? 32.5 \pm 0.1 32.0 \pm 0.1 32.3 \pm 0.1 2answers 4k views ### How to combine the error of two independent measurements of the same quantity? I have measured k_1 and k_2 in two measurements and then I calculated \Delta k_1 and \Delta k_2. Now I want to calculate k and \Delta k. k is just the mean of k_1 and k_2. I thought ... 1answer 606 views ### Is \sigma or \sigma / \sqrt{N} is error of a measurement? I wonder whether \sigma or \sigma / \sqrt{N} is error of a measurement. When I measure, say 0, 1, -1, 1, -1, I have a \sigma = 1. I just measure 0, 1, -1, I also have \sigma = 1. But in ... 3answers 3k views ### How to combine measurement error with statistic error 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 ... 2answers 215 views ### Question about uncertainty Are 3.43\pm 0.04 \frac{\mathrm{m}}{\mathrm{s}} and 3.48 \frac{\mathrm{m}}{\mathrm{s}} within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate ... 3answers 487 views ### Calculating uncertainties for a final result Say you are dividing 2 times with uncertainties:$$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$After doing the calculations you get:$$\frac{t_1}{t_2} ~=~ 0.774 \pm ...
I recently noticed that the value of Planck's constant has changed on Wikipedia. The value that I had in mind (from Google), $6.626068\cdot{}10^{-34}\text{J.s}$, has changed to ...