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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30
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8answers
6k views

Why does the speed of light 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 ...
5
votes
1answer
173 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?
1
vote
1answer
74 views

Too small error on the calculus of wavelenght

I have this function: $$\lambda=d \sin(\arctan(\frac{x}{z}))$$ and I want to find its absolute error. $d$ is a constant ($10^{-6}$), $x =(0.716 \pm 0.001)$ m, and $z=(1.000 \pm 0.001) $ m. For the ...
8
votes
3answers
114 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 ...
2
votes
1answer
128 views

How to quote answer when error is smaller than significant figures of data?

We have these rules: Can't quote answer to more significant figures than original data. Error quoted to one significant figure unless first significant digit is a one. In which case quote error to 2 ...
4
votes
1answer
251 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 ...
5
votes
2answers
139 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 ...
0
votes
3answers
677 views

Basic vector addition problem [closed]

This is the entire problem: A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant? ...
1
vote
1answer
87 views

How uncertainties affect values

If I calculate the equivalent resistance of a circuit, for example: $$1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3 = 1/1472 + 1/3260 + 1/5580 \Rightarrow R_{eq} = 858.22\,\Omega$$ And then calculate its ...
1
vote
1answer
103 views

Measurement uncertainty basics

$$x = (\overline{x}-K)\pm \Delta x\tag{1}$$ $$\Delta x = s_{\overline{x}} = \sqrt{\frac t {\sqrt n} s_x} \tag{2}$$ $$s_x = \sqrt{\frac 1 {n-1} \sum^{n}_{i=1}(x_i-\overline{x})} \tag{3}$$ $$\frac ...
1
vote
1answer
161 views

Paper in physics - calculations; rounding or not?

I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic ...
3
votes
1answer
120 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 ...
5
votes
3answers
279 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{±\ ...
2
votes
1answer
89 views

What are anticipated events and experimental uncertainty?

I am working on this lab that involved gathering data from two different sources. It involved gathering reaction times from a device and from a web application which was put into our data sets. It is ...
3
votes
1answer
668 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. ...
2
votes
1answer
170 views

Precision and accuracy calculations

Precision is usually understood as the number or significant figures in some experiment. Accuracy is the difference between the best measurement and the real value. How are precision and accuracy ...
2
votes
0answers
224 views

How can systematic errors be calculated?

Usually, it is said that systematic errors can not be handled in a well-defined way, unlike statistical errors. My question(s): A) How can systematical errors be calculated for any experimental ...
1
vote
0answers
238 views

Combining errors to calcuate the total error (standard deviations)

I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each ...
0
votes
1answer
70 views

Uncertainty in approximated relation

I'll give directly an example to fix the ideas. Suppose that you're studying the acceleration of a system of masses that depends from the number $n$ of masses $m$ by the following relation: ...
2
votes
2answers
3k views

Definition of Significant Figures

In my textbooks, significant figures are defined as: “Significant figures by definition are the reliable digits in a number that are known with certainty.” “A significant figure is the one ...
2
votes
0answers
62 views

error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
-3
votes
1answer
82 views

How many measurements should be done? [closed]

I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard deviation?
1
vote
1answer
136 views

Measurement uncertainty of the quantity, that is function of two others quantities

I'm trying to compute uncertainty for the density of the ball. I measured its radius 6 times, so I was able to compute the stastistical uncertainty (we call it uncertainty type A, I don't know, if ...
1
vote
1answer
249 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 - ...
4
votes
2answers
2k 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 ...
1
vote
3answers
197 views

Error calculation with linear regression

I am trying to determine the boltzmann constant by using a bipolar junction transistor. In my circuit (apparently I don't have enough point to join a image sorry), the Ebers and Moll model gives the ...
3
votes
0answers
160 views

Production vs. Collection, and Contaminants vs. Depositions, what might be missing in cold fusion research

I though cold fusion and LENR were discredited, but just a few days ago I found out that NASA is claiming LENR is real. So I thought if they're detecting something, what could it be, and why wasn't it ...
2
votes
1answer
245 views

Experimental measurement of volumetric flow rate

The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
2
votes
2answers
153 views

Asymmetric uncertainties

Inspired by these two question on tex.SX Asymmetrical tolerancing Asymmetric uncertainties with siunitx package I'd like to ask for a nice explanation for these kind of uncertainties, like ...
6
votes
2answers
254 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 ...
5
votes
2answers
3k 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 ...
0
votes
1answer
678 views

Two cylinders with same volume but different dimensions

If there are two cylinders (A and B) both with the same volume. B's radius is half of A's, so the length of B must be 4 ($2^2$) times that of A. The uncertainty for the radius of A is the same as ...
3
votes
1answer
122 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 ...
2
votes
1answer
100 views

Multimeter has a resistance

If a multimeter has a resistance (1M ohm, say) when measuring voltages how do I take that into account in my error?
0
votes
1answer
84 views

How can I cheat an XRD sample (~10 mg) from a total 1g required? How can I use for the background.

How much can affect (in terms of hump) my X-ray diffraction pattern the "amorphous" glass or maybe someone can suggest me other material to compensate for the small amount of the sample. Note: my ...
0
votes
1answer
62 views

Statistical error in a regression

I measured some voltage values ($x$) and some corresponding frequencies ($y$). I know that the voltage can only be measured within an uncertainty $\Delta x$. And the uncertainty of $y$ shall be ...
2
votes
2answers
2k views

When do I apply Significant figures in physics calculations?

I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of ...
2
votes
0answers
2k views

How to calculate uncertainties of a natural exponential function?

(I apologize if this should be posted in mathematics, however I chose to post it here as it's technically about physics) I conducted an experiment in which position of items were shifted on an ...
1
vote
1answer
90 views

Calculating uncertinity in measurements [closed]

I have a question relating to uncertinity.The equation used is period of a pendulum. T=2π √(l/g) For example consider time to complete 10 cycles by the pendulum as 19.6 (+/- 0.2)s. I want to know ...
4
votes
2answers
2k 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 ...
2
votes
0answers
236 views

How do I do error calculus right using gnuplot as an example?

Given is a set of measurements with their respective errors for example an energy spectrum. In gnuplot one is to fit a function $ f(x;\{p_i\})$ depending on a variable $x$ and on fit parameters $p_i$. ...
-3
votes
3answers
367 views

Significant Figures [closed]

Subtract 0.2 J from 7.26 J. Express your answer to the correct number of significant figures for the given data. I think its 7, but the answer is 7.1. HOW?
0
votes
0answers
562 views

Error Analysis, Change in momentum, Kinetic Energy

If momentum of an object is increased by 10%,then its kinetic energy will be increased by? Well, I don't need the solution logically by calculating the change in Kinetic Energy etc, but my question ...
1
vote
1answer
2k views

Calculating the Uncertainty for an Average Value [closed]

How would I calculate the uncertainty for the average of this set? $32.5 \pm 0.1$ $32.0 \pm 0.1$ $32.3 \pm 0.1$
0
votes
0answers
63 views

Piezoelectrical effect in a pendulum

How can I compute the piezo-electrical effect of a pendulum of frequency $f$ and amplitude $R$? What constants of the material will enter the computation? The material in question is an electrode on ...
1
vote
1answer
112 views

Variance of Nested Experimental Uncertainty

I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for ...
3
votes
2answers
4k 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 ...
2
votes
1answer
615 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 ...
10
votes
3answers
3k 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 ...
3
votes
2answers
220 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 ...