Questions tagged [error-analysis]

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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16 views

How to average two numbers with error bars?

I am trying to fit a function with two different data sets. Each data set gives me the fitting parameter with its error bar. How can I use these two fitting values of the fitting parameter to get its ...
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Taring a digital scale improves precision?

Suppose you need to weight something that weights $x$ in a digital scale that reads a non zero value a when empty. There are two options: Tare the scale and weight, giving $x \pm \Delta x_1$. Weight ...
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When to use Significant Figures?

When do I use significant figure rules in physics for arithmetic. I already know that I have to use it for unit conversions. Where else would I have to use it?
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Sig Figs when finding Slope

When finding the slope of a position vs time graph, do you use sig figs? for example, if the slope is 150m [N] / 10s, would the answer be 20m[N] / s (because the least amount of significant figures in ...
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how to get total Fisher matrix that makes cross synthesis of 2 Fisher matrix

I have 2 Fisher matrixes which represent information for the same variables (I mean columns/rows are the same in the 2 matrixes). Now I would like to make the cross synthesis of these 2 matrixes by ...
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What is the relation between statistical and instrumental uncertainty?

I've been studying some error analysis on An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by John R. Taylor for an introductory course. At the beginning of ...
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38 views

Dilemma in calculation of percentage error while measuring focal length on an optical bench

An optical bench has $1.5$ $m$ long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at $75$ $cm$ mark of the scale and the object pin ...
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Q. Significant figures on graphs

When displaying experimental data on a graph, must both axes use the same number of significant figures, which would be the variable with the smallest number of significant figures? Or (because a ...
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23 views

What metrics can be used to quantify underestimation of uncertainties?

Suppose an experiment measures a quantity to be $5 \pm 0.3$ and another measures it to be $9 \pm 0.3$ What metrics can be used to emphasize and quantify the error in the estimation of uncertainties by ...
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Error Propagations for Integrals and Summations

Suppose I have 3 straight lines: $$y_1 = m_1 x + c_1;$$ $$y_2 = m_2 x + c_2;$$ $$y_3 = m_3 x + c_3;,$$ and $$m_1 = 1 \pm 1.1, c_1 = 1 \pm 1.11,$$ $$m_2 = 2 \pm 2.2, c_2 = 2 \pm 2.22,$$ $$m_3 = 3 \pm 3....
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What reference clock is an atomic clock measured against?

I looked at a few of the other posts regarding the accuracy of atomic clocks, but I was not able to derive the answer to my question myself. I've seen it stated that atomic clocks are accurate on the ...
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How to define Uncertainty (instrument error analysis)?

Is it correct to define uncertainty as "The distinction between the measurements with different instruments"? Thanks :D
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Uncertainty from variable to derivative in data fitting

If I have a system of differential equations, say $x' = f(x,p)$ and a set of data $(t_n,x_n)$, where $p$ is the set of constant parameters. I can then use a fitting method like least squared to obtain ...
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Propagation of uncertainties leading to lower error in calculated product than measured quantities

I was doing a propagation of uncertainty on the following numbers, and I got a lower error from the calculated quantity than the measured quantities. So why is it that my compounded error smaller than ...
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Error in understanding error analysis

Given question: A student uses simple pendulum of length 1 m and commits an error of Δl=1mm to determine g(the acceleration due to gravity). He uses a stopwatch with the least count of 1s for this and ...
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What is the number of significant figures in $6*(7.203)**2$?

My textbook says: "In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures." but it ...
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1answer
38 views

How can multiplication rule in sigfigs make sense?

I've been going through significant figures video on khan academy and it says the product of two numbers cannot have more significant digits than the significant digits in any of the inputs. Example: ...
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How to handle uncertainty introduced by low resolution measurements

When trying to convert a continuous variable (running time of a piece of code) into a quantised one (s on a clock), I've been trying to work out the effect of instrument resolution on the uncertainty ...
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1answer
31 views

Error estimation over multiple instruments readings [closed]

A cable factory ships cables in spools of 100 km each. The overall length of each spool is known with great precision, it's 100 km sharp. In order to speed up the sale process, distance markers are ...
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Does increasing the number of readings/measurements increase the accuracy of the mean?

I understand that the accuracy of a reading/measurement is primarily dictated by systematic error and so the accuracy of your results can be improved by removing the source of the systematic error. ...
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What does the notation $8.9875517923(14)$ mean? [duplicate]

The number $8.9875517923(14)$ appears in Coulomb's constant. I have read that it has something to do with the uncertainty of the accuracy of the number but answers have been unclear. Can somebody ...
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17 views

Error in verlet and velocity algorithm

The error in position globally in verlet alogrithm is of order 2 and locally the error is of order 4 in $\delta t^{2}$. My question is in wikipidea it says the velocity is determined non-cumulative ...
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38 views

Error propagation in expression with trigonometric functions

In a physics lab inclined plane experiment, I am calculating the kinetic friction $\mu$ using the formula: $$\mu = \tan\theta - (a/g)\sec\theta$$ Here $a$ is the acceleration and $\theta$ is the angle ...
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Error propagation for quadratic

I have a very simple question I am struggling with. Lets say I want to propagate the error for some expression $$ y = x^2$$ Lets say I known that $x = 0 \pm 100$. Using standard error propagation I ...
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Should I keep significant figures constant when multiplying a number with infinite significant figures by a number with finite significant figures?

I want to multiply $\frac{1}{2}$ with $1.88 \times 10^{-2}$. The $\frac{1}{2}$ is exact and the $1.88 \times 10^{-2}$ is not. Should I write the answer as $9.4 \times 10^{-3}$ or $9.40 \times 10^{-3}$?...
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29 views

Linear fit error for beta decay spectrum

I'm trying to get an upper bound to the neutrino mass with kurie plot. In order to do that I need to make a linear fit in order to get energy value that corresponds to $y=0$. ($y$ the kurie plot). The ...
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32 views

Relative change in an oscillating quantity

Relative change (or fractional change) in a quantity is defined as the difference between its final and initial values divided by its initial value. But, what would be the relative change in a ...
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1answer
35 views

Difference between theoretical and experimental time due to gravity

This is a very rudimentary question, but I thought I would have to ask here because I don't discern any site better. Given the formula that $t$ equals the square root of $2h/g$, calculate the ...
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1answer
37 views

What is the correct way to write this uncertainty?

$$ Z = 23,8937 * 10^{-5} [u] $$ $$ u(Z) = 3,721 * 10^{-7} [u] $$ I have to write this uncertainty in complete form. Would this be correct? $$ 0.0002389 \pm 0.0003721 $$
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How to calculate uncertainty for a simple pendulum formula? [closed]

$$ T = 2\pi \sqrt{\frac{l}{g}}$$ $$U_{c}(T) =?$$ That's the only thing my teacher left me with. I don't understand how am I supposed to solve this without any measurements.
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61 views

How do you find the average of relative uncertainties? [duplicate]

If I had a set of measurements ,eg : $[10.0,11.0,11.5]$ and they each had a relative uncertainty of $10$% meaning my values are now $[10.0±1.0, 11.0±1.1, 11.5±1.15]$ how would I find the average of ...
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How to Teach Sig Figs [closed]

A few years ago I taught a physics class for 6th graders at a school with an accelerated curriculum. These students are good at memorizing, and following procedures, so I was able to teach them the ...
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Air track acceleration experiment

What can be a major error when we are calculating the acceleration of a matter, using the air track? As shown in the picture, the goal is to measure the acceleration of the matter(M). I will hang the ...
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1answer
58 views

Identifying certain digits

The result of a measurement is $57.64$ $\pm$ $0.38$ (for the sake of simplicity, I omit the measurement unit). I would know which are the certain digits in $57.64$ $\pm$ $0.38$. I know that $57.64$ ...
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How do I know if two measured variables are correlated?

Recently I've been doing error analysis and I am puzzled on how to figure out if two measured quantites are corelated. Say for example you have a lens, then you can measure 'u' and 'v'. Now would the ...
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4answers
54 views

Error analysis in implicit functions

Say you are measuring the focal length of a lens, you have the equation $$f = \left(\frac{1}{u} + \frac{1}{v}\right)^{-1} $$ Now, the error term would be differential form of this equation , as in ...
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1answer
24 views

How we calculate potential energy in best accuracy?

This question may be a bit ridiciolus but let me explain. I'm not talking about the formula, I am talking about, what is the best accuracy of calculating the potential energy. For example, let I ...
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What is the origin of the irreducible error $\propto e^{-N}$?

In this (timestamped) lecture, the professor says that any measurement includes an irreducible error that scales as $e^{-N}$ where $N$ is the number of degrees of freedom in the measurement apparatus ...
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1answer
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Calculating max percentage error using error propagation?

I was given the actual values of the modulus of elasticity of materials, and I calculated the modulus of elasticity myself using experimental data. I was then asked to "calculate the relative maximum ...
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Uncertainty in Quantum Mechanics

In Quantum Mechanics, as we know, the uncertainty is defined as $$\Delta x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}.$$ My question is - Why is uncertainty equal to the standard deviation?
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Correlations vs. negligence of correlations in covariance matrix

Suppose I have a model composed of two parameters $(a,b)$ that I want to describe a set of data points with. In CASE A, I fit the model taking into consideration the correlations between the data ...
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1answer
15 views

Calculating uncertainty using a set of measured values

I am hopelessly confused about the very basic question of how to propagate error if you want to take into consideration the error that each data point already has. For example, say I have time ...
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How to correct for finite step-size when simulating a harmonic oscillator?

I am a grad student in experimental physics and due to the Corona-lockdown, I am now tipping my toes in programming simulations. To start, I want to simulate a harmonic oscillator with frequency $\...
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Problems regarding Searle's Experiment

Recently I came across a problem on Searle's Experiment where we had to find the maximum possible error in Young's modulus calculation due to an error in the calculation of extension of string. ...
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2answers
36 views

Least decimal places rule produces ridiculous results

The rule I learnt from my physics teacher and textbook in adding numbers together was that the end result must be rounded to the least number of decimal points in the starting numbers. This makes ...
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1answer
37 views

How to determine the particles size measurement error in SEM images

I have a question that bothered me last time. I did some scanning electron microscope (SEM) on my sample which is basically array of nanopillars . My goal is to determine the pillars diameter ...
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Is uncertainty uncertain?

I was thinking about uncertainty and wondered if uncertainty is inherently uncertain. I know in the uncertainty inequality for position and momentum, $\Delta x \Delta p \ge \hbar/2$, the presence of ...
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Understanding error analysis terminology

I'm working in a lab, and the terminology in error analysis is confusing me. Lets say I have a theory that claims the fine structure constant is exactly 1/137. My current reference tells me that the ...
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Is there a graphical summary of which modulation technique to use in communication systems using Visible Light Communication techniques?

I am currently looking at various papers written (some listed at the bottom) that discuss how laser pulses can be modulated to send encoded messages to a receiver for communication systems. The more I ...
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How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

I'm dealing with the modeling of small experimental physics data sets (specifically the stickiness of glue-compounds). As most of this experimental work does not generate thousands of samples, but ...

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