Average Definition and 1000 Threads

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.

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  1. Roodles01

    Gauss Law? Average charge density

    Homework Statement Hi. A cylinder of radius r & length L whose charge density distribution is given by ρ = C/2 * r3 where r = radial distance in cylindrical coordinates C = constant show that the average charge density ρbar = a3 C / 5Homework Equations Gauss differential law div E = ρ / ε0 div...
  2. A

    Average Binding energy per Nucleon

    What is the Average/mean binding energy per nucleon of the whole periodic table/of all the elements, considering the most naturally abundant isotopes of each element? I tried googling it a couple of times but i could not arrive at a satisfactory answer.
  3. M

    Average slope of joined line segments.

    Hi! Suppose we are required to analyse the general tendency of a set of joined line segments (to increase or decrease) as shown in the figure, which would be a more accurate method? 1.) Take individual slopes of each line segment and compute the average of all such slopes. 2.)...
  4. A

    Average Potential Energy/ Oscillator

    Hi, i regard a single harmonic oszillator: $$H_{1}=\frac{p^{2}}{2m} + \frac{m \omega^{2}}{2} x^{2}$$ I know the partition function of the oszillator is: $$Z=\frac{kT}{\hbar \omega}$$ so the probability function is: $$F_{1}(x,p)=\frac{1}{Z}\exp{\frac{-H_{1}(x,p)}{kT}}$$ Now I want to...
  5. M

    Calculation of the average rate of reaction

    Hi, Im stuck: I found this example in which they calculate the rate of reaction: the title is "calculating the average reaction rate" Now how the hell is this average reaction rate if they didnt use stoichiometric coefficients!? (in this case it should be 2. Thanks in advance.
  6. X

    Average Effective Dipole moment

    Homework Statement Water relative permitivity is about 81. If the electric field E=x[V/m] (x unit vector) is inside the water, what is the vector P(dipole polarization per unit volume)? Then Assume that the density of water is 1000 [kg/m3] and that there are 3.34 × 1025 molecules per...
  7. B

    MHB Average steps required to terminate a game.

    Hii Everyone, A a box contains $N$ balls. In each step, we remove some number of balls from the box according to some distribution, where the distributions are independent but not identical. We don't know any other details of the distributions but their averages. It means in...
  8. C

    Average distance in latitude/longitude cell using Haversine formula

    Homework Statement I've constructed a 5°x5° latitude/longitude cell, from 40-45° N and 85-90°W. This puts the center somewhere near the southern tip of Lake Michigan. I'm trying to find the average distance from the center of that cell (42.5°N, 87.5°W) to any other point in that cell...
  9. T

    Average acceleration and average force

    Homework Statement Steel ball with a mass 17 grams, is launched at a speed of 6 m/s, into someones eye. The ball comes to a rest over a distance of 1mm. A) What is the average acceleration experienced by the ball to stop it? B) What is the deaccelerating force that must be exerted on...
  10. E

    How to Calculate Average Power Dissipation on a Resistor?

    1. Given that v(t) = -6 + 12 cos(2π200t + π/4) - 9 cos(2π400t + π/6) volts. The signal is applied to a 14 kΩ resistor. Find the average power dissipated on the resistor in mW. Round your answer off to two decimal places. 2. Pavg = (sqrt(Vdc^2 + vp^2/2))/R 3. I used the above...
  11. B

    Error propagation in an average of two values

    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...
  12. G

    Does Average Linkage satisfy the properties of metric space?

    Homework Statement A dissimilarity measure d(x, y) for two data points x and y typically satisfy the following three properties: 1. d(x, y) ≥ 0 and d(x, y) = 0 if and only if x = y 2. d(x, y) = d(y, x) 3. d(x,z) ≤ d(x, y) + d(y,z)The following method has been proposed for measuring the...
  13. Q

    How do you obtain electrons and know their average velocity?

    How do you obtain electrons and know their average velocity?? Hello guys! I am currently trying to experiment with charge accelerators. I soon tripped inside a really big hole. I soon realized that I didn't know how to measure the amount of charge(in coulombs) a charged conductor has. So...
  14. P

    Average IQ of a physicist/mathematician

    Hi, i was just wondering what is the average iq of a physicist? Just asking because i am only 12 yo and i really want a career in mathematics/physics.
  15. D

    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...
  16. kai_sikorski

    Moving average filter for MC solution of PDE

    I have a PDE that can be interpreted as basically an exit time problem for a certain stochastic process. I would like to use this to verify an analytical solution I've found. If I start the stochastic process at (x,y), then the average exit time from a certain region will be equal to the value...
  17. B

    How Do You Calculate Average Induced Voltage in a Changing Magnetic Field?

    Homework Statement The magnetic field shown in Figure P20.61 has a uniform magnitude of 29.00 mT directed into the paper. The initial diameter of the kink is 0.30 cm. (a) The wire is quickly pulled taut, and the kink shrinks to a diameter of zero in 55.00 ms. Determine the average...
  18. B

    Average speed of person walking

    A person walks first at a constant speed of 5.00 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 3.00 m/s. What are (a) her average speed over the entire trip and (b) her average velocity over the entire trip? I already solved...
  19. P

    Average and instantaneous velocity

    Homework Statement Given the following formula for distance, find the average velocity on the interval [1,3] S(t) = t/(1+t^2) Homework Equations Vavg = (S(t0) - S(t1)) / (t0 - t1) or Vavg = (V0 + V1)/2The Attempt at a Solution I get two different answers and I need help understand why...
  20. E

    Acceleration of a Falling Object from Average Velocities

    Homework Statement After gathering data via ticker tape, of a falling object, I had the following information: Time (s), Displacement (cm) 0.0 - 0.1 , 6.2 0.1 - 0.2 , 16.0 0.2 - 0.3 , 24.5 0.3 - 0.4 , 33.1 0.4 - 0.5 , 43.0 0.5 - 0.6 , 49.7 The Question: Determine the average...
  21. P

    The average distance between two particles in a 1d box

    Homework Statement (i) Write an expression for the wave function of 2 particles in a 1D box. Assume that their masses are the same, m, and that the box size is a = 1. What are the energy states? (Comment: The particles are distinguishable) (ii) Write an expression for the average distance...
  22. K

    What is the average drag force on a softball pitched at 99.6 km/hr?

    A softball having a mass of 0.250 kg is pitched at 99.6 km/hr. By the time it reaches the plate, it may have slowed by 10.8 percent. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is 15.2 m. F=ma...
  23. L

    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...
  24. R

    Calculating Superman's Average Force (due in 4 days)

    Homework Statement Superman (m = 90 kg) jumps over a 78 m tall building by first accelerating from rest to his maximum velocity in 0.004 s. Subsequent to this time, Superman follows normal projectile motion. What is the average force acting on Superman that gives his upward acceleration...
  25. C

    Finding time given average velocity

    Homework Statement A car travels 120km East at 45km/hr, then goes West 50km at 70km/hr, then goes East again for time t at 40km/hr. If the average velocity for the entire trip is 30km/hr East, find the time t. Homework Equations The Attempt at a Solution time of car traveling East...
  26. MarkFL

    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.
  27. C

    Clarification between average velocity and average speed

    To find average velocity, you do total displacement over total time To find average speed, you add up the speeds / total speeds there are? (Eg. (10+20)/2) Am I correct?
  28. S

    Weighted Moving Average of Cubic

    1. Show that applying a second-order weighted moving average to a cubic polynomial will not change anything. X_t = a_0 + a_1t + a_2t^2 + a_3t^3 is our polynomial Second-order weighted moving average: \sum_{i=-L}^{i=L} B_iX_{t+i} where B_i=(1-i^2I_2/I_4)/(2L+1-I_2^{2}/I_4) where...
  29. N

    Programs Average Engineering Phd Stipend?

    I was wondering if people could give me an idea of what I should expect.
  30. L

    MHB Annual Average Percentage Increase

    What is the simplest way of solving this? The value of a house is doubled in 20 years. What is the annual average percentage increase, if it is assumed to be the same each year?
  31. V

    Find the average speed from t = 0 to t = 1 s

    Homework Statement The position of a particle as a function of time is given by x = (6 m/s)t + (-2 m/s^2)t^2. Find the average speed from t = 0 to t = 1 s ---------------------------------------------------------------------------------------Also, how would I plot x versus t for t = 0 to t =...
  32. M

    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.
  33. F

    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...
  34. H

    Kinematics: finding the average acceleration

    1. Homework Statement The velocity of a particle moving along the x-axis varies in time according to the expression v(t)=α+βt2 α=46.4m/s β=4.25m/s3 t is in seconds Find the average acceleration in the time interval from t=0 to 3.63s. Answer in units of m/s2 2. Homework...
  35. P

    Average Fermion Current: Understanding the Relation to Background Fermions

    Hi! I have a little problem. Consider a 4-fermion interaction (neglecting constant factors) of the form \overline{\psi_{a \mathrm{L}}} \gamma^{\lambda} \psi_{b \mathrm{L}} \overline{\psi_{c \mathrm{L}}} \gamma_{\lambda} \psi_{d \mathrm{L}} . I want to average this interaction over a...
  36. L

    Calculating the average divergence of the flow of fluid in a box.

    Homework Statement A cube of side 5cm is placed in a fluid. For the following velocity values, calculate the average divergence of the flow. Is there a source or sink within this box? The velocities are given in cm/s. The cube is oriented so that the +z axis exits the front face, the +x axis...
  37. W

    The average temperature in the box

    Homework Statement Im not really sure were I am going wrong in the problem there was a similar one in the textbook examples with a different temperature function and they just divided by 4. I really don' t know how my integration is wrong either please help the function if you can't read it...
  38. S

    Finding the average height, z, of molecules in the box

    Homework Statement Let a box of height h be filled with classical ideal gas molecules of mass m in a constant gravitational filed g. As will be shown later, the distribution molecular height z obeys: f(z) = C exp (-mgz/KT) Where C is the normalization constant a) find the average height...
  39. F

    Find the energy lost at the collision and the average force of friction

    Homework Statement We have to make a roller coaster for our school project. This coaster starts with a spring. In this coaster, there is a collision. Essentially, I need to find the energy lost at the collision, and the average force of friction. Homework Equations Em1=Em2 W=Fd F=ma A=DELTA v/...
  40. A

    Calculus problem with average angular velocity

    A wheel has angular position theta = 0 (radians) at t = 0 (seconds). It then rotates with an angular velocity equal to .72t radians/sec. In radians per second, what is the average angular velocity from theta = 4 radians to theta = 9 radians? I got 3 for my answer but I'm not sure if it's right
  41. K

    Average thermal conductivity (?)

    Hey all, i'm trying to set up a thermal model of a permanent magnet synchronous electric motor. This by doing a lumped system analysis of the motor. In the thermal network that I've set up, I'm trying to introduce an equivalent thermal conductivity value (W/mK) for the copper conductors plus...
  42. M

    Average of a Velocity Function

    Homework Statement Given: V(n, t, x') = sin [k x' + A (n, t)] where k is a constant n stands for the nth realisation A is uniformly distributed in [0, 2pi] and x' denotes the position vector How can I show that the mean of V i.e. <V> and the mean of the squares <V^2> are...
  43. Jalo

    Statistical Physics - average energy of a system.

    Homework Statement Imagine a system, in contact with a heat reservoir, with three particles. Each particle may be in a state of energy 0 or ε. What's the temperature of the reservoir such that the mean energy of the system, <E>, is 1.2ε? Homework Equations The Attempt at a...
  44. O

    Internal energy equals to average kinectic energy ?

    For ideal gas , can I assume Cv dT = nkT (3/2) , thank you
  45. D

    Confused by "mv^2/L" - Average Force on Wall in Box

    Hey guys! I find it confusing to prove "mv^2/L", the average force acted by the air molecules on a wall in a box. My textbook tells me an assumption "the time during each molecules colliding with the wall of the container is negligible compared with the time elapsed between successive collision"...
  46. PhizKid

    Average force exerted by momentum

    Homework Statement A car of mass 10 kg hits another car at 10 m/s and they both come to rest at the same time. In the process, the car that was hit moved back 10 meters. What is the average force exerted on it? Homework Equations Average force = change in momentum divided by time...
  47. L

    Average Acceleration of a Accel vs Speed Graph

    Hi All So I have an Accel vs Speed graph and data. Goes from 0 to 80 mph. This is all the info I have. I would like to figure out what Average Acceleration would give me the same distance, of an acceleration from 0 MPH to 80 MPH. AKA, using the formula Distance =...
  48. K

    Average force to keep something in place during an automobile crash?

    Homework Statement Suppose that a seat-belted mother riding in an automobile holds a 10 kg baby in her arms. the automobile crashes and decelerates from 50km/h to 0 in .1 s. what average force would the mother have to exert on the baby to hold it?? do you think she can do this? Homework...
  49. T

    Max value of the average normal stress in the links.

    Homework Statement Here is the problem along with the solution: I am confused about part (a). Why is it that the area used is 2*0.008*(0.036-0.016). If you draw a cross section at just one of the holes, wouldn't that give you the max average stress? So the area used should instead be...
  50. P

    Power Needed for 200kg Glider to Reach 25m/s in 75m

    A glider is launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 200 kg glider from rest to 25 m/s over a horizontal distance of 75 m. Air resistance and friction are...
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