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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21 views

What's role of signal-to-noise ratio in the quantum measurement? [on hold]

Recently, I've been watching videos of MIT opencourse (http://www.youtube.com/watch?v=TcvY8Nt0ZGA&list=PLUl4u3cNGP62FPGcyFJkzhqq9c5cHCK32&index=2) taught by Nobel laureate Wolfgang Ketterle. ...
1
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1answer
24 views

Best way to estimate a coefficient when data have errors

I am a little bit confused about some tecniques concerning error-analysis.Consider this situatiuon: During an experiment I collected a $x,y$ table of data that are expected to satisfy a linear ...
8
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4answers
1k views

Can the accuracy in Planck's constant ever be increased?

I guess I am having some confusion about the history of calculating Planck's constant. I see the mass of the electron may come into the equation here but isn't the measurement of mass based mostly ...
2
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2answers
40 views

Standard convention for $x$ error bars

What is the standard convention regarding the error bars of the independent quantity in a graph? In what situations should I show the $x$ error bars? In case both $x$ and $y$ uncertainties are ...
1
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0answers
8 views

How can I estimate meta-uncertainty?

A type A uncertainty estimate is derived from repeated measurements. For example, I may estimate the uncertainty on a measurement by repeating the measurement $N$ times and then calculating some ...
1
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3answers
707 views

Theoretical uncertainty of a circuit's total resistance when made entirely of resistors

My question in short(ish) is: Will the fractional uncertainty of a circuit made entirely of resistors with equal fractional uncertainties be the same as the fractional uncertainty of those resistors. ...
0
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0answers
19 views

How is this procedure of error propagation called?

I'm calculating the error on $\theta$ from given PDG values for $f(\theta)=sin^2(2\theta) \pm \sigma_{f}$ Question: I'd like to calculate the errors (from the inverse function) as $$\sigma_{\theta}^{...
2
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13 views

Have the BaF2 scintillators a strong correlation with the alimentation current that cause the shifting of the centroids in the distribution?

In gamma gamma correlation I suspect the presence of systematic error maybe caused by a non optimal alimentation voltage according to someone there is a quadratic correlation between centroids ...
2
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1answer
40 views

propagation of error - sin^4

I am currently working on an analysis of a Rutherford scattering and encountered a somehow strange behaviour for the errors. It basically boils down to the behaviour of: $$\sin(\theta/2)^4$$ For ...
2
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1answer
455 views

Center of mass error - calculating systematic error in change in PE

Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error. \begin{align} \Delta PE = m*g*h_1 - m*g*...
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0answers
27 views

Is there a standard in the manner in which significant figures are used?

I have always understood significant figures to be those figures which we know with certainty. Wikipedia (https://en.wikipedia.org/wiki/Significant_figures) provides a related but less rigid ...
3
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1answer
68 views

Uncertainty in the distance between Sun and other planets

I have read about the orbit distances between Sun and the planets and have come to know for example: Earth is around 150 million km away from the Sun. However I have seen that tht value is only an ...
0
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0answers
16 views

Cathode Ray Tube: Nonuniform Magnetic Field

For an experiment, I found out that the charge to mass ratio of electron was 1.91x10^11 C*kg^-1. So, I overestimated from the theoretical quite a bit. I used a cathode ray tube with Helmholtz Coils ...
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1answer
75 views

Home Work Help: Calculating Entropy for Melting Ice - Clarification on answer

The question states: What is the change in entropy for the process to completely melt 8.0 kg of ice at 0°C? The formulas for Entropy we've been introduced to are: ...
1
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2answers
74 views

Error Analysis involving random errors

The question goes like this: In an experiment, the time period of an oscillating object in five successive measurements is found to be $0.52$s, $0.56$s, $0.57$s, $0.54$s, $0.59$s. The least count ...
0
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1answer
208 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 ...
4
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2answers
62 views

Combining two data points with different uncertainties

I have two separate algorithms (call them "A1" and "A2") which reconstruct the $(x, y)$-position of an event in a particle detector. I can test both of these algorithms on simulated events from a very ...
1
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1answer
30 views

Systematic+Random Uncertainty for velocity measurement

I have a question regarding systematic and random uncertainties. I have to measure the mean value of a velocity measurement in flow field at a point. I've recorded say 1000 samples in time, which I ...
0
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2answers
65 views

Least Squares Fitting - 68% Confidence Interval

I am fitting a linear polynomial to some data and I have derived the errors for each of the best-fit parameters from the covariance matrix. I would expect these errors to correspond to a $1\sigma$ 68% ...
16
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2answers
897 views

How to deal with zero uncertainties?

Suppose you measure quantity $x$ with an uncertainty ${\rm d}x$. Quantity $f$ is related to $x$ by $f=x^2$ . By error propagation the uncertainty on $f$ would be ${\rm d}f=2x{\rm d}x$. If a certain ...
0
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1answer
39 views

Is fractional error computed using the actual value or the best estimate?

I'm trying to figure out which is the best way to do error propagation for situations when you have a product. For instance, for $F(x,y) = xy$, we can use Taylor expansion and keeping 1st order terms:...
0
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1answer
48 views

Propagation error for a third grade equation

I am trying to find the value for the roots$\pm$error for a set of experimental data. The function that fit the best is $$\epsilon(t)=a+bt+ct^2+dt^3.$$ Which is the best way to calculate the roots $\...
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1answer
35 views

Error analysis / propagation : trigonometry

If the hypotenuse of a triangle is (1536 +- 3)m long, and the (non right-angle) angle measured from the ground is (22.2 +-0.1) degrees, what is the height of the triangle, and the error in this? sin(...
0
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1answer
36 views

Why is the standard deviation the error on the singular measurement?

I'm a beginner with the study in data analysis in Physics. I'm trying to understand the meaning, in the field of experimental Physics, of the standard deviation $\sigma$ of a series of data. There ...
0
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1answer
55 views

What is the accuracy when firing an electron at a target?

Consider firing an electron at a target. Let the target be at a distance $d$ and the electron be travelling at a non-relativistic speed $v$. How can we estimate the maximum possible accuracy ...
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3answers
4k views

Error calculation in parallel resistances

This is the question: There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination. According to what I've ...
3
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1answer
68 views

What does the direct sum symbol (i.e. $\oplus$) mean in the context of uncertainties

I've noticed the symbol $⊕$ used in a context I'm unfamiliar with. In several papers about the the calculation of the uncertainty of quantities measured with hadron colliders. For example the ...
4
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3answers
167 views

Why are significant figure rules in Multiplication/Division different than in Addition/Subtraction?

I've never understood specifically why this is. Here's what I mean. In Addition/Subtraction, what matters are the digits after the decimal point. So for example: 1.689 + 4.3 = ...
2
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1answer
28 views

Correction for uncertainty of multiplications and divisions

The conventional means of obtaining uncertainty of $c$ where $c = a \cdot b$ is adding percentage uncertainty of $a$ and $b$. This method seems to have a flaw as shown below (please excuse me if I am ...
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0answers
45 views

Can we calculate the point on Earth nearest to the Moon?

We have the ability to calculate the Moon's orbit in order to predict Lunar and Solar eclipses precisely. Using our known calculations of the Moon's orbits, can we calculate the closest point (city ...
3
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1answer
89 views

Measuring very long half lives accurately

There are already some questions about long half life times for radioactive elements, explaining how to calculate the half life time. Now I am wondering: When you have some radioactive material and ...
12
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2answers
19k views

How do you find the uncertainty of a weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
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0answers
26 views

Question about errors, Hubble's constant

I am just looking through some old notes I have from for cosmology, and theres something cropped up that i can't seem to figure out: Say I have two (or more) values for $H_o$ each with errors such as:...
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3answers
111 views

Given 2 values with different significant figures, how many significant figures do you take the final answer to?

A random example from the top of my head: Given a mass of $m=1.12\:\mathrm{kg}$ accelerated by $a=99.87465\:\mathrm{m\:s}^{-2}$, find the force $F=ma$. Now, how many significant would I take ...
0
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0answers
25 views

Total uncertainty of multiple stereo camera depth measurements

I have a stereo camera that measures depth for a rectangular area of pixels in a single image. Each depth measurement is obtained independently (this goes back to the stereo matching algorithm used). ...
4
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0answers
60 views

Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical ...
0
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0answers
37 views

Difference between Theoretical and Experimental Errors

When performing an experiment to find a certain value $f(x_1,x_2,..,x_n)$, we can find the error for each measured $f_i$ using partial derivatives, and we can find the experimental error $|f_i-\langle ...
2
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2answers
31 views

How do I find uncertainties in an intensity plot created from a photograph?

I have a photo of a laser beam (taken by sending the laser into a CCD). I then took the image and ran it through an image reader that gave an intensity surface plot. I then took a single cut from that ...
0
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0answers
22 views

How to calculate error in a function using partial derivative method?

I don't have error calculation using partial derivative method in my text book. Can someone explain me this method as it is quite useful in calcution of error in a physical quantity which is a ...
0
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1answer
57 views

Error propagation estimation [closed]

I have a physical quantity A defined as $A=(74.5 B^2*(M+N))^{1/3}$ where B, M, N and relative uncertainties are given. And M and N are dependent on B: $log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)$...
0
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1answer
186 views

What will be the percentage error in measurement of time?

The least count of a stop watch is 0.2 s .The time of 20 oscillationsof a pendulum is measured to be 25.What will be the percentage error in measurement of time?
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0answers
25 views

Goodness of fit for two different properties of the same model?

This is a question about statistics and optimisation. I have a model which produces two different distributions of the same dimension. Let's say they are the mean velocity distribution $\langle v(r) \...
1
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0answers
49 views

Uncertainties propagation with complex numbers [closed]

How would one go by to estimate the uncertainties on the result of a calculation when it is done with complex values ? For example I am trying to calculate the impedance of a quadrupole and the ...
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1answer
53 views

Uncertainty in Range of Projectile [closed]

If we are given that a projectile is launched with velocity 10m/s at an angle of $45^\circ$ and uncertainty in angle is of $0.5^\circ$ . What is the uncertainty in the range of projectile. The problem ...
1
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1answer
46 views

Which procedure is correct? [closed]

A problem is given in my textbook pg.no-191 as Example 5.10 A solenoid has a core of a material with relative permeability $\mu_r=400$. The windings of the solenoid are insulated from the core and ...
1
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1answer
58 views

Are residuals supposed to have error bars?

Hopefully I'm asking this in the correct section. So I've got a graph with a linear trend of data and a best fit line plotted. The data points on the main graph obviously each have their own error ...
0
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2answers
33 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
1
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1answer
24 views

How to find the error of all the counts within the Full Width Half Maximum (FWHM)?

We've been doing Gamma ray spectroscopy and have peaks from various sources. We'd use Poisson statistics, but obviously the detector doesn't have a resolution of zero, thus we are summing the counts ...
0
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1answer
70 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...
0
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3answers
93 views

Significant figures

How to calculate significant figures of a number? I got confuse as the number 28600 has 3 significant figure instead of 5. Anyone can explain?