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
Recent contents Top users
  1. Square1

    Are there better methods for finding the average value of a function?

    Hey so I am in a second semester calculus class and we are learning about the average value of the function. We are presented the following formula: (1/(b-a)) ∫a to b f(x) dx for a ≤ x ≤ b This is basically doing (x1+...xn)/n, except for infinitely many numbers over the interval...
  2. A

    Average value in superposition question

    Hi there. A quick question: When calculating the average energy (or any value) of a particle which is in superposition, why the sums have different summation index (n,m)? Thanks!
  3. T

    Average Value and Area in Polar

    Homework Statement Let Q be the region bounded by r=sin(3θ) in the first quadrant. Find the area of Q. Find the average distance of points in Q from the origin. The Attempt at a Solution I thought I could calculate area like so: \int_0 ^{pi/3} \int_0 ^{sin(3θ)} sin(3θ) dr dθ This gives...
  4. T

    Average value of a function over involving triple integral

    Homework Statement We define average value of function over a solid to be f = 1/Volume int int int f(x,y,z) dV So find the average value of the function f(x,y,z) = x^2z+y^2z over the region enclosed by paraboloid z = 1-x^2-y^2 and the plane z = 0 The Attempt at a Solution Actually...
  5. 8

    Average value of function, answer check

    Homework Statement Find the average value of the function u(x)= 10xsin(x2) on the interval [0, ∏1/2] (Sorry, I can't figure out how to make the square root symbol)Homework Equations The Attempt at a Solution For the integral of u(x), I got -5cos(x2) I substituted 0 and ∏1/2 and got 10. then...
  6. C

    Average value of sin(i) in radial velocities (exoplanets)

    When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to m\sin i\text{ where }i is the orbital inclination of the planet with respect to our line of sight and m is the planet mass. I've heard that even though the inclinations are...
  7. S

    Find the average value in a calculus approach

    Homework Statement Find the average value of : f(x) = 4sinx + 4cosx on the interval [0, 16pi/6] Average value: ? Homework Equations Integrals The Attempt at a Solution 1/ [(16pi/6) -0] ∫ from 0 to 16pi/6 4sinx + 4cosx dx [3/8pi] ∫ from 0 to 16pi/6 4sinx + 4cosx dx <------simplify...
  8. D

    Average value for the squared momentum in the harmonic oscillator

    Hi, I'm trying to resolve a problem (17-2) of Pauling's book (Introduction to Quantum Mechanics ), but I'm not achieving this integration. So, I ask for your help. The problem says: Calculate \overline{p_{z}²} (where p_{z} = momentum in z direction and \overline{x} = average value of x...
  9. I

    What is the average value of the positive y-coordinates of an ellipse?

    Homework Statement Find the average value of the positive y-coordinates of the ellipse x^2/a^2 + y^2/b^2 = 1 I don't know where to begin, please help.
  10. D

    Deriving the Average Value of a Function using the Mean Value Theorem

    Homework Statement If fave [a,b] denotes the average value of f on the interval [a,b] and a<c<b, show that fave[a,b] = (c-a)/(b-a) fave[a,c] + (b-c)(b-a) fave[c,b]Homework Equations All i know is the mean value theorem for integrals is f(c) = fave = 1/(b-a) integral(f(x),x,b,a) The Attempt...
  11. O

    What is the Average Value of a Function?

    The problem and attempted solution is in the attached document. My teacher said: "This is a confusing question. They use the word 'rate' in the description of the information. But, if you change 'growth rate' to 'something' they are asking for the average something, not the rate of change of...
  12. O

    Average Value of a Function and average velocity

    Hey quick question regarding the average value of a function; What is the difference in finding the average velocity over an interval given the position function, s(t), and the velocity function, v(t)? I don't get it?
  13. gennarakis

    Integrating sin2θ: How to Prove <sin2θ>=1/2 and <cos2θ>=1/2?

    How can <sin2θ>=1/2 and <cos2θ>=1/2 How is the proof made?Integrate sin2θ from -Infinity to +Infinity?
  14. S

    What is the Integral Average Value in Calculus?

    Hey peoplez o:) In the Fundamental Theorem of Calculus; \Delta F \ = \ F(b) \ - \ F(a) \ and \ \Delta x \ = \ b \ - \ a we can rewrite this as; \Delta F \ = \ \int_{a}^{b} f (x)\,dx Then if we multiply both sides by 1/Δx we get; \frac{\Delta F}{ \Delta x} \ = \ \frac{1}{b...
  15. C

    What is the average speed of a freely falling body starting from rest?

    Homework Statement if a freely falling body starts from rest, then its displacement is given by s = (1/2) g(t^2). let the velocity after a time T be vsubt. Show that if we compute the average of the velocities with respect to t we get vsubave = (1/2)vsubt, but if we compute the average of...
  16. T

    Average Values of Functions on Intervals

    Homework Statement i have some problems that i tried to do but i couldn't get the answer , i hope you can help me, please, 1. what is the average value of y for the part of the curve y = 3x-x^2 which is in the first quadrant? the answer is -6 , but i couldn't get it 2. the average...
  17. P

    Standard deviation and average value

    Homework Statement Students measured an object 5 times, and got the results 11,25 cm, 11,20 cm, 11,22 cm, 11,18 cm i 11,25 cm. The height of this object is: A. h = (11,22 ± 0,03) cm B. h = (11,22 ± 0,04) cm C. h = (11,25 ± 0,07) cm D. h = (11,25 ± 0,03) cm Homework Equations Standard...
  18. S

    Average Value of a Function - temperature

    Homework Statement If a cup of tea has temperature 98C in a room where the temperature is 20C, then according to Newton's Law of Cooling the temperature of the tea after t minutes is $\displaystyle \Large T(t)=20 + 78 e^{-t/50}.$ What is the average temperature of the tea during the first 38...
  19. D

    What is the average weight of water in the tank?

    Water is run at a constant rate of 1 ft^3/min to fill a cylindrical tank of radius 3ft and height 5ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by...
  20. S

    Find the average value of a function

    Homework Statement Find the average value of a function of f(x)= |x+1| sgnx on the interval [-2,2]Homework Equations The average value formula. The Attempt at a Solution I know I can divide |x+1| into two integrals from [-2,0] and [0,2] (I think?? can anyone confirm this is the proper...
  21. T

    Finding Average Value on a Bounded Region: Parabola y = 4-x^2 and x-axis

    Find the average value of y on the region D that is bounded above by the parabola y = 4 - x2 and below by the x-axis. Does this question makes sense? I know the formula for the average values function : 1/(A(x)) * doubleIntegralOf F(x,y)DA But its says above the parabola and below...
  22. E

    Find the average value of the function f(x,y)=x^2+y^2

    Homework Statement Let a>0 be a constant. Find the average value of the function f(x,y)=x^2+y^2 1) on the square -a\leqx\leqa, -a\leqy\leqa 2) on the disk x^2+y^2\leqa^2 Homework Equations The Attempt at a Solution 1) I integrated \inta-(-a) \inta-(-a) (x^2+y^2) dxdy and got...
  23. C

    Average Value of f(x,y)=sin(x+y) Over a Rectangle

    Homework Statement Find the average value of f(x,y)=sin(x+y) over the rectangle 0 ≤ x ≤ pi, 0 ≤ y ≤ pi. Homework Equations I need to know if this is the right answer please. The Attempt at a Solution I got 1/pi as a answer.
  24. E

    What is the average value of a simple harmonic function over one cycle?

    Homework Statement "A particle of mass m executes one-dimensional simple harmonic oscillation under the action of a conservative force such that its instantaneous x coordinate is x(t) = a cos(ωt − φ). Find the average values of x, x^2, x', and (x')2 over a single cycle of the oscillation...
  25. G

    Prob. for average value or less in binomial distribution?

    Hello! Is there a closed form expression or a good estimate for the probability that a binomial distribution yield the average np or less. Basically I'm asking for a good way to evaluate P=\sum_{k=0}^{np} \begin{pmatrix} n\\ k \end{pmatrix} p^k(1-p)^{n-k} I just figured that for the...
  26. D

    How is the average value for a sinewave derived?

    There's an attachment in this post, that show my attempts. So how is it actually derived for a sinewave? And if possible please debug the PDF attached. I'm sort getting the reasons for the derivation given in my book. Thanks! :smile:
  27. H

    Average value of a function and such.

    Homework Statement The voltage V in an electrical outlet is given as a function of time, t, by the function V = V0 cos(120πt), where V is in volts and t is in seconds, and V0 is a positive constant representing the maximum voltage. (a) What is the average value of the voltage over 3 seconds...
  28. M

    How do you find the average value of a function of two variables on a rectangle?

    To find the average value of a function of one variable, you integrate it and multiply it by 1/(b - a) , where b and a are the limits of integration , uper and lower, respectively. But how does one do this for a function of two variables, defined on a rectangle?
  29. A

    Average value of AC over a complete cycle is always zero

    Homework Statement Statement 1: Average value of AC over a complete cycle is always zero. Statement 2: Average value of AC is always defined over half cycle. We need to tell whether these two statements are right, and if 1 is right then whether 2 is its explanation. Homework...
  30. K

    Average Value of a Function notion

    Homework Statement In a textbook that I'm reading, the authors have stipulated that for polarized and isotropic radiation, the angle between the direction of polarization and the electric dipole vector is random, and so we can replace cos^2 \theta by its average 1/3. I cannot see how this is...
  31. M

    Are you interesting about average value if so trying here.

    Hello here you have the same question in the enclosed What is the average value? average value for (exp \alphaZ ) = \int\int exp\alphaZ ds / \int\int ds Over the sphere S: X^2+Y^2+Z^2=a^2 Also by use the parameterization X= a sinϴ cos ɸ Y= a sinϴ sin ɸ Z= a cos ϴ...
  32. N

    Average value of sin(x) integral of sin(x)/x

    This isn't a homework question by the way I was trying to think what the average value of sin(x) was between 0 and pi/2. I came to the conclusion it must be integral of sin(x)/x evaluated at those bounds. But I tried to do that in MATLAB to no avail. Any help would be awesome
  33. J

    Average Value for pulse waveform

    Heres the graph... http://img205.imageshack.us/img205/4770/graphfc6.jpg" Im trying to find the Average value for a pulse waveform... the formula is Vavg = baseline + (duty cycle) (amplitude) How do I treat the amplitude since it varies...Do I treat the cuty cycle differently as...
  34. C

    Find c for Average Value of Graph to be 0: Why c=4?

    For what value of c>0 is the average value of the graph on [-5,c] equal to zero and why? Graph is attached. I thought that that c should be 4 since at that point the areas cancel out. Not sure though. Could someone help me? Thanks!
  35. C

    Average value of a function and simple harmonic motion

    Homework Statement For simple harmonic motion calculate the average value of KE and PE in space and time using \frac{1}{t_2-t_1}\int^{t_2}_{t_1}{f(t)dt (and the similar version for space)The Attempt at a Solution For time I get <KE> = 1/4 kA^2, <PE> = 1/4 kA^2 which makes sense but for space...
  36. A

    Calculating the Average Value of cos^2(x) [0,(pi/4)]

    Homework Statement find the average value of cos^2(x) [0,(pi/4)] Homework Equations I don't think I'm doing it correctly I know the formula,(I won't put my attempt because I don't have math symbols on my computer) but I get 1 as the answer every time which doesn't seem correct The...
  37. S

    Significance of Average value of a AC signal

    [SOLVED] Significance of Average value of a AC signal Hello, I would like to know the significance of average value in a AC circuit. Let's consider a sinusoidal ac source with only a resistor in the circuit. The rms value of voltage and current indicate the equivalent DC value which would...
  38. J

    Finding Average Value of function

    Homework Statement Find the average value of the function g(x,y) = x^2 + y^2 on the region x^2 + 2xy + 2y^2 -4y =8 Homework Equations The Attempt at a Solution so far, I complete the square of the region that we want to find average value, x^2 + 2xy + 2y^2 -4y =8. And after...
  39. T

    Studying? (average value, work)

    I'm studying for a test and it would be great if i could get step by step how to do this problem: a.) Find the average value of the function on the interval x=1 to x=10 for f(x)=3/(1+x)^2 b.) A uniform cable hanging over the edge of a tall building is 40 ft long and weighs 50 lb. How much...
  40. T

    Studying? (average value, work)

    I'm studying for a test and it would be great if i could get step by step how to do this problem: a.) Find the average value of the function on the interval x=1 to x=10 for f(x)=3/(1+x)^2 b.) A uniform cable hanging over the edge of a tall building is 40 ft long and weighs 50 lb. How much...
  41. C

    Help with average value of a function

    i have a question :cry: how would you find a number b such that the average value of f(x)= 1+10x-3x^2 on the interval [0,b] is equal to 4. i have tried to set this equal to 4 but everytime i try to solve for b i get some number but it is always wrong. please help!:cry::cry::cry::cry:
  42. T

    Finding the Antiderivative of f(x) from 1 to 4 - Graph Analysis

    Homework Statement http://img296.imageshack.us/img296/7923/img0192re9.jpg The Attempt at a Solution Hope you can see what I've written on the top of the page, but basically I want to find the antider. of f(x) from 1 to 4 (from the graph I suppose). So that should be the negative...
  43. kreil

    Average value in a one-dimensional well

    Homework Statement Show that the average value of x2 in the one-dimensional well is (x^2)_{av}=L^2(\frac{1}{3}-\frac{1}{2n^2 \pi^2}) Homework Equations wave fuction in 1-dim well: \psi_n(x)=\sqrt{\frac{2}{L}}sin(\frac{n \pi x}{L}) x^2_{av}=\int_{0}^{L}|\psi(x)|^2 x^2 dx...
  44. D

    Average value of a function question

    This question popped up in my high school class today. I couldn't think of an explanation that worked for the students, other than "the definition of the average value states that the function has to be continuous on the interval." Their intuition helped them understand the definition of...
  45. T

    Proving Average Value of Gaussian Function as k_0

    The question says show that the average value of k is k_0 for the function A(k)=\frac{1}{\sqrt{2\pi}a}e^{\frac{-(k-k_0)^2}{2a^2}. I know that this is a gaussian function and that the center is k0 but i am not sure how to show this is the average value of k, what equation for average value...
  46. P

    Finding Average Value in a Weighing Experiment

    How do you find the average value in an experiment when all it consist of is weighing a beaker and adding 10 mL of water three times to it?
  47. H

    Average value of a function sent to infinity

    I was wondering if it would be possible to find the average value of a function with the only condition that x is element of R. For example, could we say that f(x)=4 has an average value of 4 since no matter what values we give for a or b in the integral from a to b of f(x)/(b-a) (b is not equal...
  48. G

    Most probable and average value of a function

    I've been asked to find the most probable and average energy of a neutron produced in a fission reaction. The neutron energy spectrum is represented by this function: \chi (E) = 0.453 e^{-1.036E} \sinh(\sqrt{2.29E}) The first part, finding the most probable energy, seems fairly...
  49. P

    How to Calculate the Average Value of a Sinusoid Over a Given Interval?

    If I had a sinusoid, how would I find the average value of it over a given interval. Say -pi/5 to pi/5 for instance. Thanks everybody.
  50. V

    Calculating Average Value of f(x,y,z) in Solid Bounded by Cylinders

    Here is the problem: First Part (already done): Find the volume of the solid that is bounded above by the cylinder z = 4 - x^2, on the sides by the cylinder x^2 + y^2 = 4, and below by the xy-plane. Answer: \int_{-2}^{2}\int_{-\sqrt{4 - x^2}}^{\sqrt{4 - x^2}}\int_{0}^{4 -...
Back
Top