Error propagation Definition and 92 Threads

Homework Statement For the equation q = \frac{z(z+2) - 2DH}{z^2} q = -0.6 \pm 10\% , and z = 0.2. D and H are known exactly. I have to find the error in z that will give an answer of q = -0.6 \pm 10\% Homework EquationsThe Attempt at a Solution I have considered rewriting the equation...

Homework Statement So I am calculating the error for something and I am getting really weird values. So I know that the value for the Inductor is 24.97 +- 0.005 mH and that for the capacitor is 105.7+-0.0005 nf. So I am finding the value for the resonant frequency Homework Equations...

Homework Statement The density of a cylinder is calculated from the following data: ##m= (2.8±0.8)g## ##d = (2.2±0.1)cm## ##h = (4.0±1.0) cm## What is the error on the density, before rounding, in ##\frac{g}{cm^3}##? Homework Equations ##V = \pi r^2 h = \frac{1}{4} \pi d^2...

Homework Statement I am taking a dataset of intensity vs. frequency (which I'll call dataset I_1), and fitting it with a linear model (I_mod). I want to divide another intensity vs. wavelength data (I_2) by this fitted model to get fractional changes in the second data set compared to the...

My goal is to find the uncertainty δd in the following equation. d=C_1 \frac{1}{\sqrt{V}} \frac{1}{D} C_1 is the collection of constants \frac{2Lhc}{\sqrt{2m_e c^2 }} D is a value measured in meters with an uncertainty δD = 0.001 m and V is a value measured in volts with an uncertainty δV =...

Homework Statement Suppose we measure N pairs of values (xi, yi) of two variables x and y that are supposed to statisfy a linear relation y = A + Bx suppose the xi have negligible uncertainty and the yi have different uncertainties \sigma_{i}. We can define the weight of the ith measurement as...

Homework Statement Not exactly a homework question, but rather a section in Statistical Data Analysis: Suppose there is a pdf y(x)[/SUB] that is not completely known, but μi and Vij are known: Homework Equations The Attempt at a Solution I understand how <y(x)> ≈ y(μ), My confusion: Why...

Hi, say I measure something ten times and get x+d1x, x+dx2, ... where dx1, dx2.. are the measurement errors. Now, say I want to calculate something from these measurements according to: A = B(C(x)), Where A is what I want, and B and C are known functions. Which is statistically...

I'm writing up an experiment I did for a lab course and I am calculating the error in quantity V. I have two runs and have ended up with a value of V for each one, as well as an error. Ie, I have V = 0.1145±0.0136 for Run 1 V= 0.1146± 0.0134 for Run 2 I got my errors through some tedious...

Homework Statement I want to know how to do error propagation on this cNi= [-(mcΔt)Al-(mcΔt)H2O]/(mΔt)Ni m is mass and Δt is change in temperature Homework Equations δc/c=√(δm/m)2+(δ(Δt)/Δt)2 The Attempt at a Solution I know the above error prop eq. above applies to c=Q/mΔt...

I am confused about calculating errors. I have learned if you take the variance covariance matrix \Sigma_{ij} of a fit of function f(x,p) to data for parameters p_i (for example by using Levenberg-Marquart) that the one sigma error interval for p_i is \sigma_{p_i}=\sqrt{\Sigma_{ii}} I only...

Homework Statement Calculate the error propagation for the theoretical effective spring constant for the two springs. The actual values don't matter, it's just supposed to show how it would be calculated. Homework Equations ke=k1*k2/(k1+k2) The Attempt at a Solution ke=A*B/(A+B) (Let...

If I have two independent variables x,y, and two measurements, m1, m2 with errors. And the dependence is thus: m_1 \pm \delta m_1 = f[x,y] m_2 \pm \delta m_2 = g[x,y] Now in my case, f and g are complicated expressions of x and y with no simple solution. (Actually I think i can...

Homework Statement This should be very simple: Given the following (boundary frequency for photoelectric effect): \nu = \frac{\phi}{h} what would be the error on \nu? Homework Equations The Attempt at a Solution \varphi and h are both determined through linear regression (y = mx + c). Where...

I was wondering if someone could please help me understand a simple problem of error propagation going from multiple measurements with errors to an average incorporating these errors. I have looked on several error propagation webpages (e.g. UC physics or UMaryland physics) but have yet to find...

Not sure if this is the right section to post this.. I have 3 measurements and was trying to take the average of the measurements and calculate the error of the average: replicate 1 = 8.9 (+/-) 0.71mg replicate 2 = 9.3 (+/-) 0.69mg replicate 3 = 8.8 (+/-) 0.70mg I get an average of 8.9333...

Not sure if this is the right section to post this.. I have 3 measurements and was trying to take the average of the measurements and calculate the error of the average: replicate 1 = 8.9 (+/-) 0.71mg replicate 2 = 9.3 (+/-) 0.69mg replicate 3 = 8.8 (+/-) 0.70mg I get an average of 8.9333...

This is an issue I am running into at the beginning of my physics course. Homework Statement Given distance and time in minutes, calculate the time in hours (part of a larger average velocity question) and graph over 170minutes. Include error bars in the graph Homework Equations...

Hi! Here is my problem: there is a star, for which we know the distance, d=21.2 pc, the measurement error is delta_d=1.8 pc. The question is that how far should we put this star, so that the following equation would be true: d/delta_d = 3? The teacher told me to use two formulas...

Okay, so I have an assignment for uni and my friends and I need to work out some info to fill out an excel document, however we're not sure exactly what it is that we're looking for. The section we're stuck on, as the title suggests, is the 'error propagation' section. Are we looking for the...

Homework Statement I was wondering if I did this right. I have to take the partial derivative of the equation below. N is an integer number having no uncertainty.Homework Equations Fc= (4pi2mn2r)/(T2)The Attempt at a Solution This is what I got as an answer with first respect to m, then r, then...

I have already turned this lab report in, but I am sure this will come up in the future. I just want to insure that I am doing it correctly. Homework Statement We did an experiment on the photoelectric effect. We found the negative voltage plateau and took readings of the photocurrent...

Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...

Homework Statement I have completed a lab that uses a Wheatstone bridge to find an unknown resistance utitlizing a resistance box and a slide wire. This will yield the unknown resistance from the following formula... Ru = unknown resistance Rs = known resistance from the resistance...

Homework Statement What are the uncertainty propagation formulas for: Area of a rectangle Density of a sphere Height of an opposite side wall calculated by tan(θ)=o/a ResistanceHomework Equations Area of rectangle= side A *side B Density of a sphere= mass/(4/3piR^3) tan(θ)=opp/adj Resistance=...

Recently I came across an example for working out error propagation, and I'm having trouble following the steps: A = 100 \pm 1% B = 10 \pm 1% AB = (100 \pm 1%).(10 \pm 1%) = \left\{1000 \pm \left[\left(100.1\%\right) \pm \left(10.1\%\right)\right]\right\} // get confused here, how does...

Hi all: In magnetic resonance imaging such as human brain head image, I select several regions of interest (ROI) with the size of 8 pixel. Thus the average value and standard deviation are computed for each ROI. Now I want to evaluate the average value over different ROIs. For example...

Homework Statement For my lab work, I have created a theoretical model that goes something like: T = \sqrt{\frac{ks^2}{x \sin \theta \cos^2\theta}} where k is a constant, and the variables to be differentiated are x, theta and s. How do I find the error of T? I can find the errors of x and...

I am doing a calculation involving taking three or more temperature measurements and then plotting them against another quantity (dependent). I get a relationship that is pretty linear, so I take the line of best fit to obtain an equation with a slope and an intercept. Now, my question is...

Hi, I am trying to represent my data in log2 form rather than "fold change" and I am embarrassed to say I can't remember how convert the error. For example, I have x=3.96 (mean), deltax=0.28 (standard dev). Thus, log2(x)=0.598. But how do I convert the error?? I know how to do it for...

Homework Statement we are trying to find the x -component of a velocity vector (V*cos\theta) our uncertainty for the velocity is +-.0003 and for the and it is .5(in degrees) how do we propagate the error for this v=.048 while \theta =27 degrees Homework Equations The Attempt...

Homework Statement Given that a puck's velocity is speed v at an angle \theta (measured in radians) with the x-axis, we know that the puck's x-velocity is v\cos(\theta). Given the error in v is \sigma_v and the error in \theta is \sigma_\theta, what is the resulting error in the puck's...

1. Homework Statement Estimate the absolute and relative standard deviations of the following calculations. The number in parentheses is the standard deviation of the preceding value. a) z=5.64(s=0.14)*log(138)(s=3) 2. Homework Equations Sx/x =SQRT((Sp/P)2+(Sq/q)2+(Sr/R)2...

Homework Statement Estimate the absolute and relative standard deviations of the following calculations. The number in parentheses is the standard deviation of the preceding value. a) z=5.64(s=0.14)*log(138)(s=3) Homework Equations Sx/x =SQRT((Sp/P)2+(Sq/q)2+(Sr/R)2 Sx=0.434(Sp/P)...

Hi, I've been trying to reproduce the output of an analytical machine here at work by doing the calculation myself in Excel but I can't get the error to match. Perhaps I am propagating the error incorrectly... The calculation is z = 2^(x-y) The values are: x = 24.96 y = 25.98 and...

Say something is a value +/- .05. What happens when you take the inverse of the value? For example, 30 V +/- .05 V. 1/V...what would the error be?

Ok, this isn't a homework question -- more out of curiosity. But it seems so trivial that I hate to post it under "General Physics" We all know the standard formula for error propagation: \sigma_f = \sqrt{\dfrac{\partial f}{\partial x}^2 \sigma_x^2 + \dfrac{\partial f}{\partial y}^2 \sigma_y^2...

Hello, I'm familiar with the common calculus approach with partial derivatives to evaluate error propagation in calculations with random variables. However, I'm looking for a way to derive the classic formula with the sum of fractional errors squared: {\left(\frac{\Delta Z}{Z}\right)}^2 =...

Homework Statement I can't seem to find online how to calculate the error propogated by trigonometric functions. That is, I know the uncertainty in \theta but am not sure how to deal with it when I apply the tan function. I am quite okay with how to deal with all the basic...

I know there is a formulas for doing error propagation with separate formulas for when dealing with powers, multiplying/dividing, and adding/subtraction. What about if I have the formula F=4*pi^2*r*m / T^2...? Also should i do error propagation for the varibles in the formula r (radius), and...

I was collecting data for a simple physics lab today when I stumbled upon a question I couldn't answer. Very basically, the lab consisted of measuring the time it takes a ball to drop a variety of distances, between 0 and 100cm. By plotting \frac{y}{t} vs. t (where y is height and t is...

Always the easy things we forget... I know how errors propogate through multiplication or division when every term has an error, but how do I propagate errors in equations when only one term has an uncertainty? I want to say just multiply and divide the uncertainty value by the constants, i.e...