# What is Average value: Definition and 107 Discussions

In colloquial language, an average is a single number taken as representative of a non-empty list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.

View More On Wikipedia.org
1. ### Average value of components of angular momentum for a wave packet

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.

34. ### Can the Average Value of an Integral Be Negative?

Homework Statement I have a question can the average value for an integral be negative. I don't see why not just checking. You know this evalutation f_ave = (1/b-a) ∫ f(x) dx Homework Equations thx The Attempt at a Solution
35. ### Average value of a function

Homework Statement Suppose we walk along a unit semicircle. Homework Equations Find the average value of our distance from the base of the semicircle. The Attempt at a Solution y_{ave} = \frac{1}{1-(-1)}\int_{-1}^1\sqrt{1-x^2}\ dx = \frac{\pi}{4} OR y = \sin\theta, \qquad 0...
36. ### Calculating the Average Value of a Function Between Two Limits

Homework Statement What is the average value of a function 1/x between x=2/3 and x=8/3? Homework Equations 1/(b-a) ∫f(x) dx with a and b being the lower and upper limits, respectively The Attempt at a Solution 1/([8/3] - [2/3])∫1/x dx 1/(6/3) ∫1/x dx 1/2 ∫1/x dx 1/2 * (ln x)...
37. ### Find Expectation Values of Spin in State |ψ⟩

Homework Statement Find expectation values ##\langle \hat{S}_x \rangle##, ##\langle \hat{S}_y \rangle##, ##\langle \hat{S}_z \rangle## in state ##|\psi \rangle =\frac{1}{\sqrt{2}}(|+\rangle +|- \rangle)## ##|+\rangle## and ##|-\rangle## are normalized eigen vectors of ##z## projection of...
38. ### Constant source Poisson eq in 2D, Dirichlet BC, average value?

Hello, for the Poisson problem Δu = -1 on a 2D circular disk with u = 0 on the boundary, we have average(u) = \frac{1}{8\pi}Area(disk), which is easy to see, as the solution is quadratic in the polar coordinate r. Does this (or a similar) relation hold for non-circular 2D domains? This...
39. ### Property of a limit of functions of average value zero in L^2 space

Homework Statement Let f_k\rightarrow f in L^2(\Omega) where |\Omega| is finite. If \int_{\Omega}{f_k(x)}dx=0 for all k=1,2,3,\ldots, then \int_{\Omega}{f(x)}dx=0. Homework Equations The Attempt at a Solution I started by playing around with Holder's inequality and constructing...
40. ### MHB Stuart's question at Yahoo Answers regarding average value of a function

Here is the question: Here is a link to the question: Find the average value of the function f on the interval [0,π]. (Enter your answer in an exact form.)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
41. ### Average value of x-coord and y-coord in a semicircle. multivariable calculus.

Calculate the average height above the x-axis of a point in the region 0 <= x <= 1 , 0 <= y <= x^2. I don't know what function to use to find the average height.
42. ### Finding the average value given the graph of the derivative

Homework Statement Since there is a graph and many things, I will post the link of my question. http://ibhl1-bccalculus.wikispaces.com/file/view/Solutions+to+optional+HL1+practice+for+final+(Larson+text).pdf Please scroll down to the last page (page 16) and my question is 6c. Homework...
43. ### How to Find the Average Value of a Function Over a Given Interval?

Homework Statement Determine the average value of the following function over the interval [0,6] f(t) = (t2-1)e-0.5t Homework Equations 1/(b-a) ∫ f(x) = {f(x)} The Attempt at a Solution Substitution? let u = (t2-1) du/dt = 2t du/2t = dt 1/(6) ∫ u e-0.5t (du/2t)And here, I reach a...
44. ### Sequences of periodic functions converging to their average value

Homework Statement Let f be a 2π-periodic function (can be any periodic really, not only 2π), and let g be a smooth function. Then lim_{n\rightarrow∞}\int^{B}_{A} f(nx)g(x) converges to \frac{1}{2π}\int^{2π}_{0}f(x) The Attempt at a Solution So far, I've come up with somewhat of...
45. ### Integrating to find average value

I have the function: f(x,y)= x*(y^2)*e^-((x^2+y^2)/4), with x and y from -3 to 3 I took the integral of this function and got 0 as my answer. I need to find the average value, which is 1/area multiplied by the double integral. Since the double integral is 0, would the average value also be...
46. ### Gaussian center not average value?

I put this under statistics because of your knowledge of the Gaussian. I have run into an elementary problem. I was considering what the average value, <x>, is for a Gaussian with an x offset, and got results which don't make sense to me. First, it is obvious that for P1(x)=e^(-(x^2)) the...
47. ### The Parity Operator: Find the average value of the parity.

Homework Statement A particle of mass m moves in the potential energy V(x)= \frac{1}{2} mω2x2 . The ground-state wave function is \psi0(x)=(\frac{a}{π})1/4e-ax2/2 and the first excited-state wave function is \psi1(x)=(\frac{4a^3}{π})1/4e-ax2/2 where a = mω/\hbar What is the average value of...
48. ### How do you find the average value of a function on a surface?

Homework Statement find the average value of (1+4z)**3 on the surface ... Homework Equations The Attempt at a Solution All I really want to know is how to go about this? Is the average value on the surface just the surface integral over the area of (1+4z)**3?
49. ### Average value for a function over its entire domain

As we know , the average value of a function over is : i wanted to calculate the average value of a function over its entire domain ( e.g ) firstly, i divided the interval into 2 intervals & and calculated the F_avg for each ,,, is my way correct ? thanks !
50. ### How do you find average value of normal acceleration?

Homework Statement Find average value of Normal Acceleration from the information given. (See the picture) Homework Equations a^{→}_{ave}= Δv^{→}/Δt a_{t}=Δv/Δt The Attempt at a Solution I took the difference of the given angles in radians and divided it twice by Δt and get...