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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43
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8answers
9k views

Why does the speed of light in vacuum have no uncertainty?

I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we ...
16
votes
2answers
893 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 ...
14
votes
3answers
893 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 ...
11
votes
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 ...
10
votes
2answers
19k views

The error of the natural logarithm

Can anyone explain why the error for $\ln (x)$ (where for $x$ we have $x\pm\Delta x$) is simply said to be $\frac{\Delta x}{x}$? I would very much appreciate a somewhat rigorous rationalization of ...
10
votes
10answers
435 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 ...
10
votes
3answers
9k 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 time....
8
votes
3answers
442 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...
8
votes
3answers
138 views

Correct expression for experimental data

I am doing practices at the laboratory. I have some doubts about how to express correctly the errors; I read some pdfs in Google but I can't solve these questions: Sometimes, it's correct to write ...
7
votes
2answers
6k views

Multiple measurements of the same quantity - combining uncertainties

I have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty. $$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm \...
7
votes
0answers
96 views

Eclipse of the sun - Intriguing luminosity curve

I've just recorded the luminosity during the sun eclipse, here is the resulting curve : Only green curve is relevant, blue curve should be ignored (it's actually the temperature). The sky was ...
7
votes
0answers
123 views

Experimentally diminishing random errors for low wavelength UV observations

Part of the work that I do involves observations of solar low wavelength UV observations, specifically UV-B and UV-A II (up to 340nm). I have noticed that when I observe responses on a CCD or CMOS ...
6
votes
5answers
1k views

Number of significant figures

I am looking for an intuitive answer that will explain me why there are only two significant figures in say the number 1500. Also definition from wikipedia: The significant figures of a number ...
6
votes
2answers
505 views

Why propagation of uncertainty is linear?

I'm in doubt with one thing: let's imagine that we have $n+1$ quantities, $n$ of them being directly measured, and the other one being related to the first $n$ by a function $f : \mathbb{R}^n \to \...
6
votes
1answer
2k views

The uncertainty of a metre ruler?

I have been taught that the uncertainty in the measurement of a metre ruler is +-1 mm. However , I was also taught that the uncertainty is half of the smallest division in the measuring instrument. So,...
6
votes
5answers
573 views

Why do the errors in a formula depend on how it's written?

Let there be an equation, let's say $V=IR$. Now when we write its error formula we write it as $$\frac{\Delta V}{V} = \frac{\Delta I}{I} + \frac{\Delta R}{R}.$$ Now let us take example values. For ...
6
votes
2answers
245 views

Why is propagation of uncertainties quadratic rather than linear? [duplicate]

1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation: if $C = A+B$ or $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = \frac{A}{...
5
votes
3answers
786 views

What does it mean to “bin” in a spectroscopy context

In the following online article http://www.star.le.ac.uk/~sav2/stats/a.html I see the word "bin" used, in relation to x-ray spectroscopy, both as a verb and as a noun (people both "bin" things and ...
5
votes
5answers
573 views

The approximate uncertainty in $r$

The volume of a cylinder is given by the expression $V=\pi r^2 h$ The uncertainties for $V$ and $h$ are as shown below $\begin{align} V&\pm 7\%\\ h&\pm 3\% \end{align}$ What is the ...
5
votes
3answers
529 views

Calculating the uncertainty of $r$, when $1/r^2$ is used

I have tried to search through the forums and the Internet, however I haven't been able to find a source I was able to understand fully. I have a distance $r$, with an uncertainty of $\mathrm{±\ 0....
5
votes
2answers
434 views

Does a large uncertainty in a given value justify a large uncertainty in the result?

I'm working on a pre-lab for my Physics 1 lab session, and I had a debate with the person I carpool with (who is taking the algebra-based Physics 1 lab). We seem to be unsure about uncertainties, and ...
5
votes
1answer
193 views

Age of the universe and age of stars

The age of the universe is 13.798±0.037 billion years, yet the age of HD 140283 is 14.46±0.8 billion years, how this can be the case?
5
votes
1answer
2k views

Propagation of uncertainty when integrating or differentiating

Lets say I have a polynomial $ax^4 +bx^3 +cx^2 +dx +e$ and the uncertainties on each coefficient. Now I need to calculate the tangent at some points as well as some areas under this curve. How would I ...
4
votes
2answers
389 views

Physical experiments - False positives

How is it made sure that something has been discovered, and not just noise? Is one discovery of something that is predicted considered to be enough (Higgs-particle)? What are the probabilities of a ...
4
votes
2answers
9k 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 ...
4
votes
3answers
163 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 = ...
4
votes
2answers
8k views

Do you round off insignificant digits in the middle of a calculation?

I have a question... Do you round with significant digits during each subcalculation of a problem or only when the entire problem is complete? Example: multiply the following number: $$1.8 \times 2....
4
votes
1answer
482 views

How do I calculate the experimental uncertainty in a function of two measured quantities

I am performing an experiment where I'm measuring two variables, say $x$ and $y$, but I'm actually interested in a third variable which I calculate from those two, $$z=f(x,y).$$ In my experiment, of ...
4
votes
2answers
58 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 ...
4
votes
1answer
260 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
4
votes
2answers
6k views

Wheatstone bridge galvanometer error

We had to measure the resistance of $R_x$, we balanced the Wheatstone bridge and did calculations. My question is: we didn't include galvanometer error into calculations. Why is that? I read that it's ...
4
votes
0answers
50 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 ...
3
votes
3answers
585 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 \ldots?...
3
votes
3answers
707 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 ...
3
votes
2answers
4k views

Calculating uncertainty in the final result (combining uncertainties)

I'm struggling to determine the uncertainty in $F$ so it would match the textbook answer. The problem statement is: A force F is obtained using the equation: $F = \frac{mv^2}{2\pi(x_2 - x_1)}$. The ...
3
votes
1answer
909 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 ...
3
votes
2answers
575 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 ...
3
votes
1answer
84 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 ...
3
votes
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 ...
3
votes
1answer
162 views

Elementary graphical error analysis

Suppose you analyze experimantal data with pencil and piece of paper, one simple method is to plot the data in a linearized way with error bars. Suppose you are interested in the slope of this linear ...
3
votes
2answers
195 views

Significant figure rules [duplicate]

In a simple physics experiment, we take the average a few readings to reduce the random errors. I apply significant figure rules to these. Say we round off at each step: (8.0+9.0+10.0)/3 = 27.0/3 (...
3
votes
2answers
524 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 ...
3
votes
1answer
61 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 ...
3
votes
1answer
1k views

Calculating Expected Systematic Error in a Pendulum Experiment

I am a little confused by part c of problem 4.28 of Taylor's Introduction to Error Analysis book. A student measures the acceleration due to gravity by using a steel ball suspended by a light string. ...
3
votes
3answers
78 views

Propagation of uncertainties

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...
3
votes
1answer
172 views

Inaccuracy at measuring gravity constant with Cavendish experiment

For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment. I set up a structure like the one suggested on this website: http://www.school-for-champions....
3
votes
1answer
39 views

Scale Factor on Error

I was gathering some data from the particle data group website and for many results it gives a value, an uncertainty and then a scale factor for the uncertainty. For instance, at here, where it gives ...
3
votes
1answer
612 views

error propagation with different plus and min errors and data fitting

I am refreshing my memory on error propagation and data fitting (Levenberg-Marquadt). You have the absolute (measurement) error, the relative (measurement) error, the population/sample standard ...
3
votes
1answer
235 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 ...
3
votes
1answer
147 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 ...