# Tagged Questions

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.

255 views

200 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 (...
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. ...
253 views

### Measuring depth or height from sea level

How is the depth or height relative to sea level measured? Well, if it's near the ocean, it can be easily measured manually, but what if it is 100 km away from the sea? What method is used?
40 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 ...
236 views

### Significant Figures in Physics

A string has linear density $10.0 \cdot 10^{-3} \, \mbox{kg/m}$ and is kept under a tension of 100 N. A sinusoidal transverse wave, with a wavelength of 0.30 m, is traveling in the positive direction ...
1k views

### Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg}$$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How ...
574 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 ...
519 views

### Combination of errors question [closed]

A resistance R is in series with an inductance L. At angular frequency ω the magnitude of the complex impedance Z of this combination is given by |Z|^2 = R^2 + (ωL)^2 . Find |Z|, and the error in |Z|, ...
221 views

### How do we find the accuracy of atomic clocks?

We say that atomic clocks are the most accurate clocks ever made, they may lose or gain $x$ seconds in $y$ years. How do we find this uncertainty because we do not have an ideal clock to compare with ...
106 views

### Weighted mean from data [closed]

Suppose we have 3 experimental groups measuring "x", they measure $$x_1=\mu_1\pm \sigma_1$$ $$x_2=\mu_2\pm \sigma_2$$ $$x_3=\mu_3\pm \sigma_3$$ In the 3 experiments, we have done N measurements of ...
86 views

### Propagation of uncertainty - proof that it is minimal

I am not really sure if this is the right SE community for this question, but, I swear, I haven't found any better. The problem is as follows: we have n distance sensors placed around a quickly ...
3k views

### What is the error in a ruler?

I'm having trouble understanding simple error analysis of a ruler. Suppose we have this ruler. There is a mark for every centimeter. The precision is half a centimeter. This should mean that the ...
669 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 ...
85 views

### Why does the rule for multiplication/division take into consideration the no. of significant figures?

I've learned that the rule for multiplication, when taking into account the significant figures, is as follows: The final result should retain as many significant figures as there are in the original ...
318 views

93 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 ...
303 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 ...
839 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, ...
1k 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 ...
51 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 ...
98 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 ...
1k 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 ...
42 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 ...
94 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 ...
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 ...
390 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 ...
148 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 ...
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 ...
38 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 + 10....
52 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 ...
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: $$\chi^2_\text{adjusted}=\sum_{k=... 1answer 786 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? 1answer 550 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 ... 0answers 124 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 ... 1answer 82 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 ... 1answer 92 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? 3answers 905 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 ... 1answer 4k 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 ... 2answers 57 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 0,01mm. then we convert the measurement to meter to be 0,01567m would the significant error ... 1answer 5k 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} ... 1answer 83 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?
$u=-10cm$ $v=10cm$ 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 A....