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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2
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4answers
77 views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
0
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0answers
13 views

error calculation with a variable error

I have to calculate the error on the following quantity: $$f(\epsilon^M,\epsilon^S)= \sqrt{ \frac{1}{N}\sum_{i=1}^N (\log{\epsilon_i^M} - \log{\epsilon_i^S})^2 } $$ Usually I would use this standard ...
2
votes
1answer
411 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 - ...
1
vote
3answers
544 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. ...
1
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3answers
131 views

Is it correct to calculate the propagation of error in this way? [closed]

I conducted an experiment and measured the values of $R$ and $H$ to calculate $v_i$. The equation used is: $$v_i=\sqrt{{gR^2}\over{2H}}$$. My average values ($v_i$ is calculated only for the average ...
0
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3answers
69 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?
0
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1answer
47 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 ...
1
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1answer
176 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 ...
0
votes
1answer
61 views

What does error order $O(t^2)$ mean? [closed]

What does it mean if something is $O(t^2)$? And more importantly, how would I check for this relationship? I thought it meant error proportional to $t^2$, and that this could be tested by plotting a ...
2
votes
1answer
102 views

Why do length measurements apparently have zero uncertainty?

In order to estimate the length $L$ of an object the distance from its edges to the $0$ of a graded ruler are measured. Assume this object has its edges at $x$ and $y$ (mean values) with standard ...
3
votes
3answers
73 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 = ...
0
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1answer
43 views

Precision of the edge of a cube versus the volume of a cube [closed]

The edge of a cube was measured with 1% precision. How is the precision of the volume of same cube calculated on the basis this measurement? Is it true that precision of the measurement would be 3%?
0
votes
1answer
48 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
0
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1answer
44 views

The confusion of fractional error calculation

I need to find the focal length of a lens by using equation 1/u + 1/v=1/f I have: u= 50+-3 mm v= 200+-5 mm I calculate the value of f as 40mm. Now i need to find the uncertainty in this value. ...
6
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1answer
1k 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. ...
1
vote
2answers
46 views

Error propagation without analytical expression

I have an algorithm $f$ that takes two inputs $x,y$ and gives one output. I say algorithm because I don't have the analytical expression for $f(x,y)$ (it's a black box in a computer, surely a ...
-1
votes
1answer
84 views

error propagation of a quantity [closed]

I have $e =$ 0.015 $\pm$ 0.005. How would I use error of propagation to calculate the uncertainty on $$ \frac{1}{( 1 - e^2)^{\frac{1}{8}} } $$ EDIT Since the question was put on hold then I will ...
1
vote
1answer
510 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
0
votes
0answers
26 views

Systematic error of constant speed

Given a constant unknown speed $m$ and $n$ data samples of (position, time). Performing a linear regression yields $y = mx + c$, and a statistical error on $m$ and $c$. I already have this values. ...
0
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0answers
19 views

Calculating the error with Cramer's Rule

I am trying to calculate the error in the function $A=\frac{\det{A_1}}{det{A}}=\frac{y_1^{'}\alpha_2-y_2^{'}\alpha_1}{y_1\alpha_2-y_2\alpha_1}$ but unfortunately every method I attempt is giving me an ...
2
votes
4answers
61 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
93 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 ...
0
votes
1answer
62 views

How can we calculate statistical uncertainty on number between 0 and 1? [closed]

Lets suppose I have zero events in data. And Monte Carlo predicts 0.5 events. If I take square root of 0.5 to report statistical uncertainty on MC prediction, it comes out to be $\pm0.707$. This means ...
0
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0answers
33 views

Position from acceleration, or acceleration from position, to track an object moving the speed of sound

I'm working on a project that involves tracing the motion of a fast-moving object (approx the speed of sound) through a fairly defined trajectory. Would it be more accurate to measure the position of ...
6
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0answers
88 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
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0answers
121 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 ...
1
vote
1answer
28 views

Error propagation rounding [duplicate]

hope I am right in this section. I am unsure with error propagation. When calculation the error in a titration, many errors has to be taken into account: Error in Glassware/ Error in Balance/ Error ...
1
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2answers
108 views

Use of normal distribution in measurement error theory

When you study an experimental results you assume that normal distribution describe random error, specially in lab courses in K12. Is this true for every random component error treatment in physics? ...
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1answer
84 views

Error propagation with dependent variables

Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra where each channel with $f(y)$ counts has error $\sqrt{f(y)}$. ...
1
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1answer
27 views

Residuals are normally distributed

I did not know whether to post this question in the Physics or Statistics section of StackExchange, but the question involves the application of statistics to the analysis of experimental results. I ...
2
votes
1answer
36 views

Confirmation of Uncertainty in Indices New Formula? [closed]

I am experimenting relations with regards of the value with uncertainty raised to the $n$th power. I came up with this formula: $$(A\pm\alpha)^n=A^n\pm(A^{n-1}n\alpha)$$ Anyone here able to ...
3
votes
1answer
145 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 ...
0
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0answers
113 views

Calculating accuracy, error, full scale error, relative error and more in a specific case

I recently bought a O2(oxygen) sensor and I am trying to figure out the error in the percentage O2 (O2pct, unitless but in %) output value that it gives out. This error is not stated in its data ...
1
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1answer
45 views

Error in total counts

I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t. Later on I take the total count rate. (Number of counts/time: $N/t$) I'm supposed to find ...
3
votes
1answer
103 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: ...
5
votes
3answers
739 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 ...
0
votes
2answers
30 views

Filament lamp $(V,i)$ behavior between 0 and 1V

I was wondering why the behavior is more "chaotic" at 0~1V when compared to 2V+ (which is when it starts to glow).
-1
votes
1answer
114 views

Mass loss for Fusion energy? [closed]

I am thinking how you can estimate the mass loss of the fusion energy for 1 kWh. I think you cannot use Einstein's $E=mc^2$ to calculate the mass loss in the fusion reaction of the Sun. How can ...
1
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1answer
38 views

Error Propagation for Bound Variables

Say I'm trying to calculate the energy term Pressure*Volume based on measurement of P and V over many different trials. Given a constant temperature, pressure and volume are bound variables as PV=nRT ...
1
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1answer
3k 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. $\frac{\Delta R}{R^2} = \frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$ ...
8
votes
3answers
318 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 ...
0
votes
1answer
64 views

Why is drag neglected while dealing with kinematic problems?

Why is drag neglected while dealing with kinematic problems? While dealing with problems related to finding velocity, acceleration and other kinematic problems, it is mentioned to "neglect drag". ...
1
vote
0answers
45 views

Error propagation for products [duplicate]

Suppose you have two measured (independent) physical quantities $x$ and $y$ with relative errors $r_x := \frac{\delta x}{x}$ and $r_y := \frac{\delta y}{y}$, where $\delta x$ and $\delta y$ are the ...
1
vote
1answer
102 views

Error propagation for exponents

I was told that since $x^n = x\cdot x\cdot x \cdot \ldots \cdot x$ that the error is $$\delta f = f_{\text{best}} |n|\lbrace \frac {\delta_x}{f_{\text{best}}} \rbrace$$ where $f$ is a function of ...
9
votes
2answers
14k 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 ...
0
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2answers
38 views

Which 'error' to choose random or absolute?

WIn the experiment, to measure the distance I used a ruler (the least digit is 0.5 cm) For each idep. variable step I repeated the experiment 10 times, and then calculated the standard deviation ...
0
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0answers
35 views

Basics of experimental error 'bookkeeping'

In scientific experiment, I know that it is very important to know the exact level of error contained in a result, but I am not sure what the correct procedure is to 'keep book' of these errors. I ...
2
votes
1answer
43 views

Measurements and errors

I've measured several values of $V$ and $I$ in a simple circuit to determine de value of a resistance $R$: $$R=\frac{V}{I}$$ I have a list of points $(V,I)$ with their corresponging error (from the ...
2
votes
3answers
70 views

Why aren't calculation results in error propagation at the center of the range?

We have two copper rods, with $L_1$ and $L_2$ as their lengths respectively, and we want to glue the two bars together, with glue that's infinitesimally thin. $$\begin{align} L_1 &= 20 ± 0.2\ ...
4
votes
2answers
5k 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 ...