Techniques and methods for computing, estimating, or placing bounds on the errors of expressions (formulas) based on knowledge of error distributions, error intervals or bounds of variables and parameters entering those expressions, and of methods used in the computations.

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Is there uncertainity of position of the perfectly homogenous radiating body? [on hold]

I heard the standard interpretation of Heisenberg Uncertainty Principle: Just the measurement affects the position of the body because allways you want to see the body (=to measure the position), you ...
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1answer
23 views

Energy resolution of LHC Electromagnetic Calorimeter

So I am trying to get an estimate of the electromagnetic calorimeter resolution at LHCb, and I have found this online: But I have no idea of what it means. Can anyone explain what the last part ...
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20 views

Calculating errors?

Hollow cylinder of length l, inner and outer radii r1= 2.5+-0.3mm, r2= 5.5+-0.3mm, density= 7.88g/cm^(3), mass density= p, mass= (pi)xpxlx(r2^(2)-r1^(2)). What is the mass?
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1answer
48 views

Resolution of experiment is lower than the detector, so how to weigh the data?

I am attempting to create an atomic model based on data from a transmission electron microscope (TEM). Basically you shoot electrons at bunch of identical molecules stuck to a grid, and look at the ...
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2answers
37 views

Which error propagation equation to use for a function of 2 variables?

So I have been taught two formulas for error propagation: For $Z=A+B$, $\sigma_Z=\sqrt{(\sigma_A^2+\sigma_B^2)}$ and for Z=AB or Z=A/B ...
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1answer
48 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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1answer
40 views

How should I calculate uncertainty of measurement calculated as average of two measurements

I am measuring force with two channel transducer. Both channels (separately) of this transducer has been calibrated and I can calculate uncertainty of measurement for each of it. However I want to ...
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2answers
106 views

Percent error calculations dilemma

I have a set of experimental results for calculating g: 9.82 9.52 10.77 10.39 9.75 9.79 10.13 10.56 10.26 9.84 10.07 9.58 These were taken using a pendulum experiment. My dilemma is that, ...
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1answer
62 views

What is logical way to calculate percentage error?

I wish to know logic behind percentage error formula. Say, $A$ is measured or calculated quantity, $B$ is theoretical or known or benchmark quantity. Then, what should be the formula for percentage ...
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27 views

Maximum error of number of observations within several certain intervals – Accuracy of variable is known

I have carried out a series of measurements of different thermal comfort parameters from which I have calculated another variable called PMV. My data set consists of hourly measurements (and ...
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1answer
34 views

Numerical Error Propagation

I'm doing the common experiment of determining $ g $ by means of a simple pendulum, and I've decided to do so by measuring the period of the pendulum at variable lengths. I've had no problems ...
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1answer
91 views

Frictionless Cart on a Ramp (Experimental Design Question)

Question: Why is the calculated value for our final velocity higher than our predicted value? Since our prediction neglected air resistance and friction, shouldn't the velocity for the actual cart ...
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30 views

Uncertainty of measurement with goniometer

I got a goniometer with scale -90 to 90 degree. I use only 0 to 90 degree. One section of the scale has 1 degree. I read a value of $62^\circ$. What is the uncertainty of this measurement? I thougt ...
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15 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
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3answers
37 views

Can a piezo actuator have infinite resolution?

See here: http://www.omega.com/googlebase/product.html?pn=LD400-1&gclid=CjwKEAjw77OhBRCJ7Onfp_HNtwYSJACZqHAWVTfW1BO4RSfSVjz9P3Q4FoPTvZ2r3NIc2W1uEthVhBoCgUHw_wcB I don't think so. Do they just ...
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0answers
28 views

Propagation of Error Formula

I did a lab, and found the Hall voltage for different currents. From these, I was also given the direction, and magnitude of the magnetic field. I need to find the number of charge carriers per ...
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1answer
32 views

How can I find an error formula for density? [closed]

$${p} = \frac{4m}{πtd^2}$$ How can I find the error in this formula? I don't know where to begin. I know that I'm looking for the "partial derivative" of density to solve this, but that is a brand ...
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2answers
127 views

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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1answer
70 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
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1answer
32 views

Error limits when we have 4 lengths adding up and then finding its mean?

I have the following readings for length of a wire: 10.2 ± 0.1 cm 10.3 ± 0.1 cm 10.1 ± 0.1 cm 10.2 ± 0.1 cm Now, when I find out the mean value, I get: (10.2 ± 0.1 + 10.3 ± 0.1 + 10.1 ± 0.1 + ...
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43 views

What is the error on measuring the phase of a sine wave?

Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t) = 1 + A \sin(\omega t+\phi)$$ where $A < 1$. I have measured this wave N times, and we can assume these ...
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1answer
53 views

About $\chi^2_\text{adjusted}$ [closed]

I am reading "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by J. R.Taylor", and I read the following formula in an exercise: ...
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1answer
67 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
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1answer
62 views

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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54 views

Background subtraction for a signal ans Errors Analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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45 views

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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1answer
43 views

What is the experimental uncertainty of an ensemble measurement? [duplicate]

Let's say you measure the time it takes for 10 oscillations of a mass undergoing simple harmonic motion to within ± 0.01s, what is the uncertainty of the period of one oscillation?
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3answers
482 views

What limitations are there in measuring physical properties accurately?

In a StackOverflow answer, I attempted to explain why a 32-bit float was perfectly adequate for representing the questioner's weight measurement: Physical properties are inaccurately measured ...
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1answer
434 views

How to find percentage error of equivalent resister? [closed]

The resistors of $R_1=100\pm3Ω $ and $R_2=200\pm4Ω $ are connected in parallel.Then express equivalent resistance with percentage error. I know how tho find percentage error if resistors are ...
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2answers
48 views

Significant error conversion

So here is my question: Say we have measured something to be 15,67 mm and the significant error is $\pm 0,01$mm. then we convert the measurement to meter to be 0,01567m would the significant error ...
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1answer
625 views

Relative error of equivalent resistance of resistors in parallel

I just saw a formula in my book for relative error in equivalent resistance of two resistors connected in parallel. $\frac{\Delta R}{R^2} = \frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$ ...
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1answer
56 views

Significant Figures (rules of addition)

It is a simple one but different teachers answer this question differently. $$34+1.4+0.2$$ what would be its answer with due regards to significant figures?
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154 views

Calculation of error in focal length? [closed]

$u=-10cm$ $v=10cm$ Using the formula the focal length is 5 cm. But how do I get the fractional error in focal length when neither $\Delta u$ nor $\Delta v$ are specified? The options given are ...
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3answers
131 views

Chaos theory deterministic or non-deterministic?

While i was studying about chaos theory, i stumbled upon this, When a ball confined in a square, and at the center is located a circle, is to bounce elastically, the path of the object deviates ...
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1answer
166 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
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2answers
109 views

What's the difference between average absolute error and relative error?

I am quite confused by both these terms. I would like to know what's the exact difference between both these terms and which one is more accurate.
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0answers
34 views

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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1answer
51 views

Significant digits of time divided by 10

We're testing the period of a pendulum in physics class by measuring the time it takes to complete 10 periods then dividing that by 10. Our timing equipment measures to the nearest 100th of a second. ...
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0answers
25 views

Sum of independent errors [duplicate]

During a physics lab we stumbled upon a little problem. The measuring device was unstable, oscillating between two values. We were told to write down the average with the half-difference between the ...
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1answer
39 views

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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1answer
41 views

What is the correct way to handle significant figures when calculating compound uncertainties? [duplicate]

When processing experimental data, and calculating an uncertainty value in multiple steps, should intermediary uncertainties be used to a certain number of significant figures or kept to the full ...
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10answers
313 views

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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2answers
110 views

How to calculate error of parallax and sextant based navigation?

First of all, why wasn't the sextant ever used for land navigation? The horizon is easier to see at sea, but land based sextants could be used in conjunction with artificial horizons (as at sea when ...
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1answer
93 views

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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1answer
90 views

Error propagation of statistical error

I have a pulse profile (binned photon counts versus phase) of a star, and for each count rate I have its statistical error. I want to calculate the so-called pulsed-fraction ...
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1answer
36 views

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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5answers
91 views

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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2answers
152 views

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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1answer
124 views

Combining uncertainties - multiple measurements

I am trying to understand how to combine uncertainties when they are dependent and independent from each other. Using this formula : $$\delta z = \sqrt {\Biggl(\dfrac{\partial f}{\partial x} \delta ...
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2answers
264 views

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 ...