Error Definition and 998 Threads

An error (from the Latin error, meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake.
In statistics, "error" refers to the difference between the value which has been computed and the correct value. An error could result in failure or in a deviation from the intended performance or behavior.

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  1. kq6up

    Error Estimation for Mary Boas Series Problem 1.14.8

    Homework Statement This is problem 1.14.8 in Mary Boas: Math for Phys. Sci. Estimate the error if f(x)=\sum _{ n=1 }^{ \infty }{ \frac { { x }^{ n } }{ { n }^{ 3 } } } is approximated by the sum of its first three terms for |x| < 1/2 . Homework Equations Error\quad <\quad...
  2. C

    Mathematica Solving ODE numerically in Mathematica - 'ndnum' error?

    I'm trying to solve this ODE R'(t)=\frac{-a}{R(t)^2} numerically in Mathematica (a, b are non-zero constants). Here's what I have: NDSolve[{R'[t]==-a/R[t]^2, R[0]==b, WhenEvent[R[t]==0, end=t; "StopIntegration"]}, R, {t,0,1}] It's returning with NDSolve:::ndnum : Encountered...
  3. PhanthomJay

    E to the -y plus trial and error math?

    A co worker has the following equation: 3e^{-.5y} +3e^{-y} + 3e^{-1.5y} + 103e^{-2y} =98.39 Solve for y. Some sort of compound interest bond equation I am told, or something like that. He has been told that to solve for y, one must use a trial and error approach. True??
  4. D

    Error in Carroll's Spacetime Geometry?

    On page 161 of Carroll's Spacetime and Geometry, Carroll writes that \delta g_{\mu\nu}=-g_{\mu\rho}g_{\nu\sigma}\delta g^{\rho\sigma}. ##\delta g_{\alpha \beta}## denotes an arbitrary, infinitesimal variation of the metric. Why is there a minus sign? By the regular rules of raising and...
  5. Harry Smith

    Determining error in a linear gradient/slope

    Hi, so I'm currently writing a lab report and need to determine the error in the value of my graphs gradient, m. I have found the maximum and minimum gradient from the 'worst' lines of fit but am lost where to go from there. My data analysis/statistics lecture notes are no help on this topic...
  6. adjacent

    Fix oledlg.dll Error: Re-Install Program & Download DLL File

    This message appeared when I logged in today.It came from Internet download manager and Adobe reader. which are set to auto-start on user start up. I manually tried to open Internet download manager and still got the same error. I have never seen such a thing. I suspect this is caused by...
  7. J

    Calculating Relative Error of Measurement: (1±0.1)cm or (1±10%)cm?

    Hello, If I have a measurement of 1cm, and have an absolute error of 0.1 cm, I know that I can write my measurement as (1±0.1)cm. If I want to write it with its relative error instead of an absolute error, can I still use the bracket? i.e) (1±10%)cm ? Thank you!
  8. C

    Percentage Error of Equilateral Triangle Perimeter

    Triangle ABC is an equilateral triangle with side 4 cm long which is measured corrected to the nearest cm. Find the percentage error of the perimeter of triangle ABC.The Attempt at a Solution Is [(0.5 x 2 x 3) / 12] x 100% correct? the '2' here is the measurement errors of the starting pt and...
  9. E

    Estimate the error variance of Autoregressive model

    Hi everyone, hopefully someone can help For an vector AR(1) model of the form y(t)=Ay(t-1) + et How does one estimate the variance of the white noise input. I was under the impression that one can simply use the residual of the model fit and estimate the variance from this, when I do a...
  10. evinda

    MHB Find Relative Error of A: 2.33

    Hey! :rolleyes: I have also an other question :o Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$ I have to find the relative error for $A$. We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the...
  11. S

    Fortran FORTRAN error array bound is not scalar integer

    FORTRAN error "array bound is not scalar integer" I'd like to know if a loop can be created, inside which I can call a subroutine in which there are arrays to be defined whose size varies as a function of loop variable. I tried as following, but got error "array bound is not scalar integer"...
  12. M

    MHB Maximum error for the Lagrange interpolating polynomials

    Hey :o ! Could you help me at the following exercise? $k, n \in \mathbb{N}$ $f(x)=cos(k \pi x), x \in [0,1]$ $x_i=ih, i=0,1,2,...,n, h=\frac{1}{n}$ Let $p \in \mathbb{P}_n$ the Lagrange interpolating polynomials of $f$ at the points $x_i$. Calculate an upper bound of the maximum error...
  13. M

    Solve Error in Integrating z^2lnz from 0 to 2

    Homework Statement ## \int_0^2 z^2lnzdz ## 2. The attempt at a solution ## u = lnz, dz = zdu, lim_{t→-∞}\int_t^{ln2} ue^udu ## ## lim_{t→-∞}ue^u - e^u l^{ln2}_t ## ##2(ln2 - 1) - lim_{t→-∞}\frac {t-1}{e^{-t}} ## Using l'Hospital's rule: ##2(ln2 - 1)## This is incorrect though...
  14. N

    Calculating Mean Square Error with Pseudo Inverse Approach

    Find the mean square error using the pseudo inverse approach. I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?
  15. evinda

    MHB Upper bound of the relative error

    Hello! :) I am looking at the following exercise: Let the linear system $Ax=b$ with $\begin{pmatrix} 2.001 & 2\\ 2& 2 \end{pmatrix}$ ,$b=\begin{bmatrix} 2.001 &2 \end{bmatrix}^T$ and y an approximate solution,so that $Ay-b=\begin{bmatrix} 0.001 &0 \end{bmatrix}^T$ .Find an upper bound of the...
  16. J

    If you have any further questions, feel free to ask.

    So I am a little confused about how to calculate the error uncertainty of a slope. Let's say I have data points (1,2), (2,2.75), (3,3.75), (4,4.7), (5,5.5) which when put in excel gives me a slope of .895. Let's say the error uncertainty for every point is +/-0.1. What I used to do is subtract...
  17. J

    How to Calculate Absolute Error Correctly?

    calculate the absolute error of a) 0.0342 m +- 5% b) 0.0342 m +- 0.5% Did I do these correctly? a) 0.342*.05=1.71 so round it to 2 m b) .0342*.005=1.71 (there was a 10^something after these numbers on the calculator) so round it up to 2 meters again Did I do those correctly?
  18. T

    Fortran [Fortran 90/95] Error: function has no IMPLICIT type

    Hi! I get an error when trying to compile my program: test8.f95:26.8: BMat = BMatScal(InverseJacobian, ShapeFuncDeriv) 1 Error: Function 'bmatscal' at (1) has no IMPLICIT type I don't know why it complains because I specified type of the function in its definition (please see...
  19. I

    Correct my simple error (property of scalar multiplication)

    say i have some vector ##\vec{v}## multiplied by a scalar k. the norm of ##\vec{v}## would be just ##||\vec{v}||## and the norm of ##k\vec{v}## is claimed to be ##|k|||\vec{v}||## ie, ##||k\vec{v}||=|k|||\vec{v}||## ie the sign of the constant is irrelevant. when i work it out...
  20. J

    Error uncertainty for power law

    So I have a series of 5 data points let's say that they are (1,1),(2,3),(3,4),(4,4.5),(5,4.75) that create a power function that has the equation y=1.2x^.97. Let's also say that the error uncertainty for every number is 0.1. I know that for a linear line you can take the uncertainty of the...
  21. M

    Mathematica Solve Error in Mathematica: Get Solution Here!

    Here is my code Nl = 10^(49) ; Nh = 100 ; b = 4*10^(-13) ; Rs = N[((3 Nl)/(4 Pi b Nh^2))^(1/3)]; a = 6*10^(-18) ; Solve[x/(4 Pi r^2) E^(-Nh a x) a Nl == (1 - x)^2 b Nh, x]When I run it, it shows the error: "Solve::nsmet: This system cannot be solved with the methods available to Solve. >>"...
  22. U

    MHB Met Office mean average temperatures and margin of error

    I have been debating with a few other people on another board, regarding the correct way to calculate the mean average of a list of values, where those values are recorded temperatures. A great many people seem to believe, for example, that if each temperature reading is accurate to +/- 0.5°...
  23. K

    Limit proof that 1=0 - Where is the error?

    Limit proof that 1=0 -- Where is the error? \lim_{n\to\infty } 1=\lim_{n\to\infty }\frac{n}{n}=\lim_{n\to\infty }\frac{\overbrace{1+1+\ldots+1}^{n \text{ times}}}{n}=\lim_{n\to\infty }\frac{1}{n} + \lim_{n\to\infty }\frac{1}{n} + \ldots=0 I have a feeling it is in the step where you split...
  24. Crush1986

    How to Calculate Building Height Using Speed of Sound and Physics Equations

    Homework Statement A physics student with too much free time drops a water melon from the roof of a building. He hears the sound of the watermelon going "splat" 2.50s later. How high is the building? the speed of sound is 340 m/s. Ignore air resistance. Homework Equations D= Vt (to find how...
  25. N

    Potential energy: where is the error in my logic?

    1) For gravitational potential energy: ##F(r)=-\frac{\gamma M m}{r^2}##. 2) For potential energy of a conservative force-field: ##-\nabla E_p = F##. So the gradient of the potential energy is always equal to the force in that direction, just with the opposite sign. So when you move in the...
  26. N

    Calculating the Percentage Error in Measurement Uncertainties

    Homework Statement Let x=5.234+/-0.0005 and y=5.123+/-0.0005. Find the percentage error of the difference a=x-y when relative errors deltax=deltay=0.0001. Homework Equations I think a=0.111 because 5.234-5.123=0.111 and +/-0.0005 cancel each other out. But how do I find the answer from...
  27. K

    Calculators Unexpected Result on TI-89 Titanium for Equation with Negative Exponents

    I was working with a much longer equation and receiving a result I didn't expect, and finally narrowed it down to the following section: 2(-2^3)-3(-2^2) 2(-2^3) is correctly calculated as -16 independently, and 3(-2^2) is correctly calculated as 12 (again, independently) for a difference...
  28. M

    Archived Weighted least-squares fit error propagation

    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...
  29. S

    Solve for Error in ∫√(16-9χ²) dx: Step-by-Step Guide for Success

    ∫√(16-9χ²) dx this is what I tried let 9/16 χ² = sin² then x=4/3(sinu) and u=arcsin(3/4x) and dx=4/3(cosu) du ∫√(16(1-sin²u) )x 4/3(cosu) du ∫16/3 cos²u du ∫8/3(cos2u + 1) du 4/3(sin2u) +8/3 u +k 4/3(2sinucosu) +8/3 u +k 8/3...
  30. G

    LAB: Bragg Diffraction Grazing Angle Error

    Homework Statement I wasn't sure where to post this question. I hope I picked the right section of the forums. This is from intermediate lab. The lab is for Bragg diffraction using microwaves. The grazing angle is a measured quantity along with the voltage (which was measured using an...
  31. Superposed_Cat

    MATLAB Solving MATLAB Duplication Error with For Loop

    Hi, I'm totally new to MATLAB and tried this for loop for K = 1:10 disp(abs(tan(K))) end it displays 1.5574 2.1850 0.14255 1.1578 3.3805 0.29101 0.87145 6.7997 0.45232 0.64836 1.5574 2.1850 0.14255 1.1578 3.3805 0.29101 0.87145 6.7997 0.45232 0.64836 Why did it display...
  32. perplexabot

    How to Connect Source to Body in PMOS Layout?

    Hello all. I have been at this layout all day and I have seriously had it. So half way through the day I realized and confirmed that it is the source to body connection of the middle pmos that is missing (i think), the problem is I don't know how to make that connection! Simple, but I have tried...
  33. L

    Please help find my error with this velocity diagram?

    Homework Statement Find piston velocity and Find angular velocity AB about A. I apologise if the image is poor! If very bad I'll elaborate in writing the values... Homework Equations Draw a velocity vector diagram to solve the above. Also use 2∏RPM / 60 to convert crank speed...
  34. I

    Error of Simpson's, Trapezoid, etc. Rules

    I learned this a while ago in my calculus 2 class and I was just thinking about it... Where do these error equations for each of the approximation rules come from? Like for example, where does the error for the Simpson's rule, $$|E_{S}|\le \frac{M(b-a)^{5}}{180n^{4}}$$ come from? Also, why even...
  35. J

    C/C++ [C++] COMPILER ERROR: error: expected ']' before ';' token

    [C++] COMPILER ERROR: "error: expected ']' before ';' token" I'm getting 3 errors on the line usi bA_indx_val = _booArr[indx/USI_BITS]; denoted in my code. error: expected ']' before ';' token error: expected primary-expression before ']' token error: expected ';' before ']' token Can't...
  36. Q

    Displacement (Answer Key Error)

    Homework Statement The position of an object traveling in a straight line at time t is given by s(t) = (2/3)t^2 + 4t^2 + 6t + 2. What's the displacement after 3 seconds? Homework Equations Displacement is final position minus initial position. The Attempt at a Solution Displacement at...
  37. B

    Reoccurring Error in RLC Series Circuit Problems.

    Hi All, In doing some practice RLC series circuit question, I have been obtaining incorrect values for active and reactive power. The magnitudes I obtain are correct however the sign of the value is not. I have attributed this to obtaining an incorrect argument for the absolute power, or...
  38. P

    Error in Y-intercept, Least-square+Excel=True?

    Homework Statement What is the error of the y-intercept and gradient of a fitted line? The line is fitted to some number of data points each with a known error in the x and y values. More specifically, I have fitted a linear equation to some data points using Microsoft Excel LINEST, and the...
  39. A

    Use DE to show error percentage

    Homework Statement Use Differentials to show that an error of 2% in the measurement of the side of a square results in an error of approximately 4% in the calculation of the area Homework Equations I'm using Area =(sΔx)^2 The Attempt at a Solution Using Δx=0.02, Area=...
  40. NATURE.M

    Question on the error of the estimated mean.

    So I took a series of measurements, where the reading error for the measurements are either ±0.01 mm or ±0.02 mm or ±0.03 mm or ±0.04 mm. Now, I can calculate the estimated mean of the measurements by x_est=Ʃ x_i / N, where x_i is the i th measurement. Then I can propagate the errors in the...
  41. A

    Add Error Bars to Individual Points in Excel 2008 for iOS

    Hi, Okay, I'm in a bit of a rush: Can you put error bars on INDIVIDUAL points in Excel? I found the "custom" setting for the error bars, but you can only add custom error bars for ALL points. I'm looking for a way to mark errors for each point individually. Is there any way to do that? I...
  42. P

    Solving Interpolation Error w/ ≤ 5*10-8 Precision

    Hi, Homework Statement Interpolation for the function f(x)=cos(x) for evenly distributed values of x in [0,π] (h=xi+1-xi, xi=ih, i=0,1,...,πh) is carried out. Also known are f(xi). I am asked to determine the value of h so that the interpolation's error is ≤ 5*10-8. Homework Equations...
  43. U

    Error Propagation - Estimating Variance

    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...
  44. K

    MHB Asymptotic error formula for the trapezoidal rule

    I need to use the asymptotic error formula for the trapezoidal rule to estimate the number n of subdivisions to evaluate $\int_{0}^{2}e^{-x^2}dx$ to the accuracy $\epsilon=10^{-10}$. I also need to find the approximate integral in this case. I would like to know if my attempt is correct. Thanks...
  45. S

    Help with error analysis ly needed

    Help with error analysis! urgently needed Homework Statement Using the theoretical prediction of t, find the errors of both t and x, . The problem is based on an experiment I did in Labs, In which a small metal ball was fired at 40° (uncertainty 0.5°) to the horizontal, at a height,y= 1.095m...
  46. G

    Why Do Significant Digits Include Uncertain Numbers?

    Homework Statement How many significant digits does the number 3568 +/- 42 have? Homework Equations The Attempt at a Solution The true value is ranging between 3526 and 3610. Why is there two significant digits and not one? I can't even find a specific definition of significant...
  47. C

    Java Java error with variable initialization

    import java.util.Scanner; import java.io.FileNotFoundException; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; public class CountryPopulationReverse{ public static void main(String args[])throws FileNotFoundException { //Variable...
  48. D

    MHB Diagnosing an Error in my String Wave Solution

    My plot seems wrong so I am not sure what the problem is: (a) mistake in sol (b) mistake in coding. A clamped, uniform string under tension \(T\) has length \(\ell\). The string is struck in the middle, giving an initial tranverse velocity distribution \[...
  49. S

    Fixing a Math Error: How to Identify and Correct Mistakes - Quick Help Request

    Hello, Please view attachment! Thanks!
  50. M

    Fortran Fortran runtime error: End of file

    Dear all, I want to read file "d1.dat": 1.025000+7 5.794453+0 1.050000+7 5.770080+0 1.075000+7 5.750135+0 1.100000+7 5.734860+0 1.125000+7 5.724448+0 1.150000+7 5.719060+0 1.175000+7 5.718829+0 1.200000+7 5.723865+0 1.219440+7 5.730802+0 1.225000+7 5.732945+0 1.250000+7 5.743325+0...
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