# What is Uncertainties: Definition and 167 Discussions

In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.The measurement uncertainty is often taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative measurement uncertainty is the measurement uncertainty divided by the absolute value of the measured value, when the measured value is not zero.

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2. ### Finding percentage and absolute uncertainties

the answers to other parts of the question: a, 2.0×10-⁷ b, 40 N c, O.O5 d, 4×10⁹Pa I Really don't understand how to solve the e part I Know that Young modulus= (Force÷Area)÷(Extension÷Load) kindly guide how to solve this question.
3. ### Error propagation leads to different uncertainties, which do I choose?

I understand how to compute and propagate errors but have trouble with conceptualizing all things put together. I have performed an experiment to determine a value for some quantity. This quantity depend on two variables. The first one depend in turn on some other quantities as well but I think...
4. ### I'm getting two possible uncertainties for frequency

Calculate the speed and uncertainty in the speed for a wave with wavelength ##50\pm 3\mu s## and frequency ##30\pm 1kHz##. Also calculate the period and uncertainty in the period. I am not sure about my answer to the second part. I used propagation of errors to get ##\Delta...
5. ### I Systematic uncertainties in linear fit

Hello! I have some data points ##(x,y)##, with some uncertainties on y that are statistical ##dy_1## and some systematic ##dy_2##. I want to fit this data using a linear function. How exactly should I deal with the different types of uncertainties? Can I just add them in quadrature and perform...
6. ### A Piecewise linear interpolation with uncertainties

Hello! I have a function ##y = f(x_1,x_2)##, and I would like to do a piecewise linear interpolation. However, both the dependent (##y##) and independent variables (##x_1, x_2##) have uncertainties associated to them (the uncertainty is the same for a given variable i.e. all ##x_1## measurements...
7. ### I Uncertainties from linear interpolation

Hello! I have a function of several variables (for this questions I assume it is only 2 variables), ##y = f(x_1,x_2)##. I want to learn this function using simulated data (i.e. generated triplets ##(x_1,x_2,y)##) and then use that function to get ##y## from measured ##(x_1,x_2)##. There is no...
8. ### Propagating Uncertainties in acceleration when using a video software

Here's why I'm confused: I recorded a video of a ball moving across the floor and uploaded it to the video analysis software I used. I had to track the moving ball while it moved and I did this while the video was playing in slow motion through the video analysis software. put a dot in the...
9. ### A Uncertainties on Bayes' theorem

Hello! I have a setup consisting of some charged particles each of which is produced at a different position, ##(x_i,y_i,z_i)##. I don't know the exact position, but I know that each of the 3 variables is normally distributed with mean zero and standard deviation of 3 mm. What I measure in the...
10. ### Uncertainties in climate models

I have seen that many posters here seem to be very knowledgeable about the man made climate "emergency". So someone can surely point out a reference where all the sources of uncertainties for at least one specific model are provided with an estimate of their values (for examples, uncertainties...
11. ### I Multiplying Uncertainties in Different Units

I could not find any clear explanation on multiplying quantities with different units while including their uncertainties. For example, how would you compute the following product with their uncertainties? 3.4 Newtons +/- .12 Newtons x 1.7 seconds +/- .23 seconds
12. ### Calculating Numerical Uncertainties in an Equation

Background Information: I am working on a pulsed NMR lab project that involves graphing out a semi-log graph of free induction decay amplitude as a function of time. After graphing out the semi-log graph, I am to determine the apparent spin-spin relaxation time (##{T_2}^*##) through the...
13. ### A Monte Carlo to compute uncertainties, why report the mean and SD?

I am learning about the use of Monte Carlo to calculate/estimate uncertainties. If I take the example of a single measurement (i.e. I measure several quantities required to get an estimate of some physical property, but I do this only once), I can use Monte Carlo and some common sense for the...
14. ### Python Solving an Integral equation with uncertainties

I have some variables that are uncertain, these are w_m = u.ufloat(0.1430, 0.0011) z_rec = u.ufloat(1089.92, 0.25) theta_srec = u.ufloat(0.0104110, 0.0000031) r_srec = u.ufloat(144.43, 0.26) and some constant values c = 299792.458 # speed of light in [km/s] N_eff = 3.046 w_r = 2.469 *...
15. ### I Statistic uncertainties in cross section plots - how to calculate?

Hi there, I hope I chose the right forum for my question. So, basically, I'm doing an analysis measuring the number of signal particles in a certain momentum bin i, and doing two corrections: Nsig, i=M*(Nmeas, i-Nbkg, i) Here, M is a matrix covering PID correction and PID efficiencies, and...
16. ### I Right way to account for non-statistical uncertainties

Hello! I have data from a spectroscopy experiment of the form ##(\lambda,N)## where ##\lambda## is the laser wavelength and ##N## is the number of photon counts for that given wavelength. The structure of the obtained spectrum is pretty simple, having a few peaks that need to be fitted with a...
17. ### I Uncertainties of the hadronic corrections for electron and muon

The pie chart in this link shows that about 99.95% of the total error of g-2 of the muon in the theoretical prediction is due to the uncertainties in the hadronic corrections. What is this number for g-2 of the electron? Maybe this number exists also for tau particles? The new value of fine...
18. ### Sigfigs and Uncertainties

A thermometer which can be read to a precision of +/- 0.5 degrees celsius is used to measure a temperature increase from 30.0 degrees celsius to 50.0 degrees celsius. What is the absolute uncertainty in the measurement of the temperature increase? Do sigfig rules for addition and subtraction...
19. ### A Combining model uncertainties with analytical uncertainties

This is my problem : it all starts with some very basic linear least-square to find a single parameter 'b' : Y = b X + e where X,Y are observations and 'e' is a mean-zero error term. I use it, i find 'b', done. But I need also to calculate uncertainties on 'b'. The so-called "model uncertainty"...
20. ### Confused about how to find the mean of uncertainties for pendulum exp.

I'm confused about how to find the final value of g and its uncertainty. I've done a bit of research and I have encountered conflicting information, some say you have to weight the measurements, some say you have to find the standard deviation then divide by two, etc. I have the following...
21. ### Uncertainties in a set of measurements

Suppose I measure the distance between two objects for three trials. The two objects then get farther away, and I measure the distance between them again for three trials. I repeat this for 3 more different distances, getting a total of 15 measurements (3 trials for 5 distances). I then compute...
22. ### B Combining uncertainties (error propagation)

Hi! I was wondering how would I calculate the uncertainty of a value that is calculated using both multiplication and division? For example, with something like: Q = mc(T2 - T1) I'm not sure what to do with the uncertainties for T2 - T1 uncertainty = Δm/m + Δc/c + (ΔT1 + ΔT2)/(T1 + T2) Or...

24. ### How to compare two measurements with uncertainties in terms of sigma?

Perhaps that statement is just saying how big the t-value is. Like, in this case: t = (1.0 - 0.98) / 0.1 = 0.1 So we can say that our measured value is within 1 sigma from the other measured value. In this case, do we just ignore the uncertainties of the other measured/reference value? It's...
25. ### Uncertainties and the angle of minimum deviation

Homework Statement For a physics experiment I need to find the uncertainties and I am using the angle of minimum derivation formula: The value of A=60° and one of the values of D is 29.7° which has a uncertainty of ±2 (I know it's a very high value) Homework Equations How do I calculate the...
26. ### How do I find refractive index uncertainties?

I've been doing an experiment where I've used prisms and a spectrometer to find the exact angles inside the prisms and the refractive index of the prisms by finding the minimum angle of deviation. I have attached a picture of the formula I've been using to find the refractive indices. Where...
27. ### MHB Solving Uncertainties: Explaining My Mistakes

Hello, I've been doing this quiz that is mostly based around uncertainties. I've got a few questions that I've got wrong, and was wondering if someone could give each a brief explanation. There's a few to go over, so if you'd be willing, I would be very grateful. I've had a crack at these...
28. ### Questions on Uncertainties

Hello, I've been doing this quiz that is mostly based around uncertainties. I've got a few questions that I've got wrong, and was wondering if someone could give each a brief explanation. There's a few to go over, so if you'd be willing, I would be very grateful. I've had a crack at these...
29. ### A What are the typical uncertainties of data in Astophysics?

Hello, everybody. I'm conducting an investigation in planetary sciences. Specifically in exoplanet detection by the radial velocity method and I'm stuck because I need to know how to defend the data that I'm using. I'm using the data from http://exoplanet.eu/catalog/ and I have found some data...
30. ### A Question about data & Monte Carlo statistical uncertainties

Hi I was wondering the following/feeling uneasy about it: Does it make sense to separate the statistical uncertainties of data and Monte Carlo? For example assume infinite statistics in your MC (uncertainty-->0) while your data is finite : so they come with some "uncertainty" (if that makes...
31. ### I Why do systematic uncertainties disappear using ratios?

Hello, I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty". I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...
32. B

### I Uncertainties and significant figures

If I have a result that can only be quoted to 2s.f., let's say 20, and I calculate an uncertainty of 0.2, then how do I quote this?
33. ### Uncertainties - reading errors

Homework Statement Hi, I have a question about uncertainties. If I am carrying out an investigation I need to record my uncertainties in each measurement. I am aware that instruments have reading errors. So, if I use a stopwatch to measure the time period of a pendulum the reading error is...
34. ### Mastering Uncertainty Calculations: A Guide for Lab Courses and Beyond

Hello, took a year off school and starting school soon. So I'm shaking off the rust and remembered in my previous lab courses we were supposed to compute uncertainties but I never really understood how that works. All I remember was its something to do with pythagorean theorem. I want to really...
35. ### Uncertainty of the function? My answer is a bit different

Homework Statement Homework EquationsThe Attempt at a Solution The answer is different though,
36. ### I Calculating error on averages with uncertainties in meas.

Let's say I take 3 measurements, and each measurement has its own uncertainty: M1 = 10 ± 1 M2 = 9 ± 2 M3 = 11 ± 3 I want to quote the average, and the net uncertainty. I understand that the uncertainty of the mean is: (Range)/(2*√N) where there are N measurements. So: (11 - 9)/(2*√3) = 1/√3...
37. ### B Can %age uncertainty in value ever be greater than 100?

We were given an experiment in which the %age uncertainty of majority of students happened to be greater than 100?
38. ### Relative Uncertainties

Homework Statement How can I calculate the relative error of a laser beam waist and angle of divergence using this experimental data: I have measured the increase in laser beam diameter as the distance from the laser increases. With this data I plotted a graph of distance from the laser beam2...
39. ### How to calculate the average with uncertainties?

Homework Statement How to calculate the average given the uncertainties in each measurement 8.70 +/- 0.28, 9.680 +/- 0.046, 9.700 +/- 0.055, 9.720 +/- 0.067? Homework EquationsThe Attempt at a Solution I know I add the values and divide by 4. I also know I add the absolute uncertainties but...
40. ### I Computing uncertainties in histogram bin counts

I am working on astrophysical data and I have a large number of redshift values of quasars. Now, each redshift estimate comes with its estimated standard error naturally. If I plot a histogram of these redshifts, I would expect the bins counts to also have some sort of uncertainty. I am unable...
41. ### How do I calculate uncertainties for this experiment?

Homework Statement I used error propagation equation to calculate errors in x and y for each individual data. Error in y is negligible. My goal is to find the uncertainty in the gradient. 2. Homework Equations The plotted equation is eV=h\frac{c}{2dsin(\theta)} ,where Plank's constant, h, is...
42. ### Percentage Uncertainties Question

Homework Statement Been given a problem where a force (F) is applied on a circular area (m2). If the percentage uncertainty of the force is 8% and the percentage uncertainty of the radius is 3%, what is the percentage uncertainty of the obtained value pressure? Homework Equations I know that...
43. ### Calculating Wavelength Using Diffraction Grating

Homework Statement A common method for finding wavelength is to use diffraction grating. The relationship between wavelength λ and the angle of max intensity θ for first order interference is λ = d*sinθ where d is the spacing between lines on the grating, which is the inverse of the grating...
44. ### A Statistical uncertainties of sub-backgrounds

I was given a code that generates the statistical or systematic uncertainty of different sub-backgrounds to the total background... Let's say that the total is N and each sub-background has N_i, \delta N_i number of events and relative uncertainty (=err/Nevt) respectively. What the code does is...
45. M

### A Uncertainties in Poisson processes

Good morning PF, I'm feeling a bit doubtful about this issue. I'm working with optical detectors and I have to characterize them in terms of quantum efficiency and other similar things. Now suppose my detector is, ideally, a single large pixel, which I illuminate for a specific time. Then I...
46. ### I Calculating semi-major axis and minimum mass of an exoplanet

Hello guys, I'm doing my physics coursework on kepler's third law and I'm finding the minimum mass and semi-major axis of a unknown planet. I have the following data: Stellar mass Mstar = 1.31 ± 0.05 Msun Orbital period P = 2.243752 ± 0.00005 days Radial velocity semi-amplitude: V = 993.0 ±...
47. ### What is the Uncertainty of Human Hearing Frequency?

what can be the uncertainty of the frequency that humans can hear ? I'm aware that there are many ways,but i tried google-ing to find them but i couldnt. if you could help me it would be great.
48. ### Calculating % uncertainties

A manufacturer needs to determine the volume of metal used to produce a metal pipe of the following dimensions: Length, L 40 + 1 m External diameter, D 12.0 + 0.2 cm Internal diameter, d 10.0 + 0.2 cm Estimate the greatest possible percentage error of the volume. the correct ans is...
49. ### Linear system control with unmatched uncertainties

Hi everyone, I have a problem about linear system control with unmatched uncertainties, the system is \dot{e}=Ae+Bu+w where \dot means differentail sign, u is the control input, w is the disturbance, A is already Hurwitz, is there any way to design u such that the disturbance w can be offset...
50. ### Signal to noise ratio and uncertainty in magnitude

1. The problem statement, all variables and given/known dat Show that if you have a signal f and noise σf for a stellar flux measurement, then the uncertainty on the observed magnitude is given by σm = 1.0875 x σf / f Homework Equations (you should use the fact that when ε<<1 then log(1±ε) ≈...