# 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.

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### 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%?
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### 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 ...
142 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. ...
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,...
51 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 ...
89 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 ...
32 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. ...
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### 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 ...
83 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, ...
164 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
370 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? ...
182 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 $\sqrt{f(y)}$. ...
40 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 ...
40 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 ...
201 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 ...
85 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 ...
192 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....
797 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 ...
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### 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).
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### 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 ...
195 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 ...
80 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". ...
53 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 ...
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### Have the BaF2 scintillators a strong correlation with the alimentation current that cause the shifting of the centroids in the distribution?

In gamma gamma correlation I suspect the presence of systematic error maybe caused by a non optimal alimentation voltage according to someone there is a quadratic correlation between centroids ...
150 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 $(x)$...
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### 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 ...
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### 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 ...
49 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 ...
459 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 ...
80 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\ \...
1k views

### error propagation with an integral

My question here is about how to determine the error of an integral given individual uncertainties in two parameters defining the function being integrated. I used a curve fitting function to ...
93 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?
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### how to handle errors in this high-school experiment?

I'd like to conduct some measurements with my pupils in the high-school I'm teaching in, but I ran into some conceptual problems. I'd like to measure the (approximately constant) speed $v$ of an ...
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### Error propagation log2

I have a quick question to report some numbers on an experiment. I made measurements of fluorescence in a titration of a chemical. The titrations were 1:2 serial dilutions so I report each ...
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 ...
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 ...
72 views

### Is there a maximum accuracy for positions in the universe?

I was thinking how, since an object in our universe can move from one position to another, it must have passed through all the positions between those two positions. (I am thinking it moved it a ...
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### How can we calculate the standard deviation of multiple values with different uncertainties each?

For example, if I have a set of readings, like: 13.4 +/- 0.5 14.5 +/- 0.7 12.8 +/- 0.6 13.9 +/- 0.4 14.8 +/- 0.5 How do I calculate the standard deviation of ...
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### Not direct/inverse proportion implies systematic error

We were doing error-analysis and my physics teacher said: A relationship between physical constants is either direct proportion or inverse proportion. If these are not true then there is a systematic ...
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### # significant figures in calculations?

I was taught to use the same number of significant figures in my answer as the piece of data with the lowest number of significant figures, so I was a bit confused when the solutions manual for this ...
46 views

### Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
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### Simple question relating to physics prac reports

I am writing a physics practical report relating to the elasticity of materials relating to their momentum in a collision. I have values for the elasticities that are all within 2% of each other but I ...
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### How to understand the uncertainty of quoted value of cosmic black body radiation?

Geiner's Quantum Mechanics - An Introduction quotes a alue of cosmic black body radiation, "$2.65 \pm 0.09 K$". How to understand this uncertainty? I have undergraduate mathematics degree and are ...
4k views

### Error calculation in parallel resistances

This is the question: There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination. According to what I've ...