What is Average: Definition and 1000 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.

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  1. A

    Solving an Energy Problem: Calculating Average Molecule Energy Through a Hole

    Hello everyone. I was hoping someone could help me out with the following problem. I tried working it out, but I don't know if I did it correctly or if I missed an important point. It just seems too "short". it would be much appreciated if someone could go through my solution quickly and give...
  2. C

    What is the average of a random hemispherical distribution

    Hello, I'm trying to write a monte carlo simulation for an optical analysis. Half the area of a sphere is within 60 degrees of the poles. Hence, I'm assuming half of randomly directed radiation should fall within 60 degrees of the poles, when radiation is generated at the center of the...
  3. M

    MHB Cost Functions for a Firm: Marginal & Average Cost

    The cost function of a firm is given by C(x) = 300x - 10x^2 - 1/3x^3. A) Find the Marginal Cost Function B) Average cost function C) The output at which marginal cost is equal to average cost.
  4. R

    Time average in a continuum probability distribution

    Homework Statement I have a question that looks so stupid that I have never dared to ask. If I want to measure the time average from t=0s to t=1s of a given f(t), the solution is compute the following integral: TA = 1/T*∫F(t)dt However, I have some doubts about this calculus.Homework...
  5. J

    Average number of different colors of marbles in a sample?

    Hi, I'm asking this in relation to samples of DNA amplicons, but I'm so confused by probability, that I think it would be easier for me to understand in terms of simple marbles-in-bag situation. Say there is a bag of 10 different colors of marbles in equal amounts, and you are allowed to pull...
  6. A

    Calculating average force - momentum problem

    Homework Statement A golf ball is struck by a golf club at 55 m/s at an angle of 28.0° above the horizontal. The mass of the ball is 45 grams and is in contact with the golf club for 15 ms. Calculate the average force exerted on the ball by the club.Homework Equations pi + FΔt = pf p = mΔv a...
  7. U

    Zeeman Effect - average shift is zero?

    Homework Statement Part (a):Find the first order shift in energy Part(b): What is the degeneracy after perturbation? Find Show average shift in energy is zero. Homework Equations The Attempt at a Solution I've shown part (a), the troubling part is part (b). Part (b) With the perturbation...
  8. B

    Average Net force and high jumpers

    Homework Statement A high-jumper with a mass of 65kg just clears a height of 2.13m and drops onto a 0.30m thick landing mat. a) What average net force does the landing mat exert on the high jumper if it is compressed by 0.18m during landing? b) What would be the effect on the force if the...
  9. T

    Average energy mass on a spring

    Homework Statement Hi, I hope this isn't a silly question. I am looking to find the mean potential energy of a mass on a spring with spring constant k and maximum displacement x0. Homework Equations The Attempt at a Solution I know the maximum energy is 1/2*kx0^2 so would the...
  10. O

    Average power in Amplitude Modulation

    Homework Statement how the overall power becomes lesser when one side band is taken away by the bandpass filter and also how it limits the bandwidth of the signal Homework Equations The Attempt at a Solution there is will be the trade off between power and bandwidth. Vdc and Vm...
  11. B

    Average kinetic energy/ temperature confusion

    My mcat book says temperature is a measure of the total kinetic energy of a system. Then later on it says temperature is a measurement of the average kinetic energy of a system. Is this an error? Thank you.
  12. S

    What is the average separation of these molecules?

    The number of molecules per cubic metre of air at standard temperature and pressure is about 2.7X10^25 / m^3 . What is the average separation of these molecules? I know the number of molecules is derived from the equation pv=nRT.But what does average separation of molecules mean and how do i...
  13. Z

    Maximum average power for a purely resistive load

    Homework Statement Consider the circuit shown in the figure below. Suppose that R = 46Ω and Z=j14Ω. Determine the maximum average power that can be delivered to the load if the load is pure resistance. Note that the voltage source magnitude is given as Vmax, not VRMS Homework Equations j =...
  14. P

    Average momentum squared of Psi(100) of hydrogen atom

    Homework Statement Calculate <p2> for ψ100 of the hydrogen atom Homework Equations ψ100 = 1/(√pi) (1/a0)3/2 e-r/a0 0∫∞ r n e-B rdr = n!/Bn+1 p2 = -hbar ∇2 = -hbar2 (r2 d2/dr2 +2 r d/dr) (ψ does not depend on ø or θ) The Attempt at a Solution<p2> = ∫ψ*(p2ψ)dV ∫dV = 4pi0∫∞r2dr <p2> =...
  15. kelvin490

    Average Power of A.C.: Assume Phase Difference Zero?

    We know that the average power of A.C. is IVcosθ, where I and V are RMS and θ is the phase difference. I would like to ask in common application, such as power of a lamp, computer, fan etc. Can we simply assume the phase difference is zero and get a fairly accurate answer? Thank you.
  16. C

    His average speed for the first 4km is what?

    A man runs a distance of 9km at a constant speed for the first 4km and then 2km/h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4km is what? Total distance = 9km Total time = 1 h For the 1st for 4km, he moved at a constant...
  17. B

    Deriving Average Energy Function For A Classical DOF

    Hello everyone, The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243 However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?
  18. V

    Engineering Calculating Maximum Average Power of AC Circuit

    Homework Statement Homework Equations The Attempt at a Solution The text in the black box looks wrong to me. The method below is how I would do it. Why is it wrong? $$To\quad maximize\quad power,\quad \overrightarrow { Z_{ L } } =\overrightarrow { { { Z }_{ th } }^{ * } } \\ \\...
  19. R

    Ideal 1/4 mile time from Average Power

    I'm wanting to get the time it would take a vehicle to travel a 1/4 mile coming out of a corner in the ideal world. By ideal I mean that I'm assuming there is no energy loss to friction, wheel slippage, drag, or heat. I want to avoid using gear ratios, and since it is an ideal world I'm assuming...
  20. D

    How can we calculate the average power of a conventional AM signal?

    Homework Statement Trying to calculate Conventional AM average transmitted power of the modulated signal s(t) = A (1+ka m(t) ) cos(2∏f t) where A: carrier amplitude ka: amplitude sensitivity m(t) : message signal f: Carrier frequency my professor's lecture notes calculate the average power as...
  21. T

    Average value of current from graph.

    This isn't exactly homework, for which I am not posting in the homework section. I am currently doing my undergrads, and am in the second semester of my first year. I am going to give my finals which start from tomorrow, with the first subject being Electrical Circuits II. I was solving the past...
  22. T

    Calculate Average Emf in Rectangular Coil

    Homework Statement A rectangular coil of wire has 65.0 turns and is 30.0cm by 43.0cm . Initially the plane of the coil is perpendicular to a uniform external magnetic field. It is then rotated till its plane is at an angle of 35.0∘ with that field. The magntude of the external field is 1.90T...
  23. Y

    I am having a problem with this question - average speed of a car

    Homework Statement a car travels along a straight path at a constant speed of 60mi/h for a distance d and then another distance d in the same direction at another constant speed the average velocity over the entire trip is 30mi/h what is the constant speed with which the car moved during...
  24. A

    Average Acceleration of a Motorboat

    Homework Statement A motorboat traveling in a straight line has a velocity of +4.0 m/s at some point in time. After 5.0 seconds, its velocity is +7.0 m/s. What is its average acceleration during this time?Homework Equations avg accel.=change in velocity/change in time The Attempt at a...
  25. S

    What does it mean to use the integrator as an average?

    Hello all, I'm going through Foundations of Mathematical Analysis by Johnsonbaugh and Pfaffenberger, and I read a curious line that I was hoping someone here could clear me up on (perhaps I'm thinking too much into it). The begininning of the section on the Lebesgue integral introduces a...
  26. M

    How often on average - shooting arrows into 2 targets

    how often on average -- shooting arrows into 2 targets Hello, I was playing a game the other day as an archer. There were two possible setups and ever since i have been trying to decide which one is going to be the best. So here goes. option A: You fire 3 arrows, they have a chance x to...
  27. L

    What is the average value of an observable in a quantum system?

    Why we define that average value of some observable ##\hat{A}## in state ##\psi## is ##(\psi,\hat{A}\psi)## Why this isnot perhaps ##26(\psi,\hat{A}\psi)##?
  28. E

    Just a few questions - calculating the average speed and John's speed

    Normally I would ask my teacher, but since we had the day off and it's due the day we get back, I can't question him. Homework Statement What is the difference between calculating the average speed and John's speed (questions g and f)? and how do you find displacement for a distance-time...
  29. A

    Calculating average inflation rate per year

    Homework Statement An economist has predicted that for the next 5 years, annual inflation will be 8%, and then there will be 5 years at a 6% inflation rate. This is equivalent to what average price change per year for the entire 10-year period? Homework Equations The Attempt at a Solution...
  30. I

    Real vs Average Power: Which is Correct?

    So I was reading through my course's lecture slides and it appears to contradict. In one slide it states that the average power, P = VrmsIrmsCos(phi) in another slide it states that the real power, P = VrmsIrmsCos(phi) Which one is correct?
  31. M

    Average kinetic energy of a damped oscillator

    For a damped mechanical oscillator, the energy of the system is given by $$E = \frac{1}{2}m \dot{x}^2 + \frac{1}{2}k x^2$$ where ##k## is the spring constant. From there, I've seen it dictated that the average kinetic energy ##\langle T \rangle ## is half of the total energy of the system. This...
  32. C

    Average Velocity and resultant velocity

    A hiker begins a trip by first walking 25.0 km south east from her base camp in 8 hours. On the second day, she walks 40.0 km 60.0° north of east in 12 hours, at which point she discovers a forest ranger's tower. Determine the average velocity of the hiker Determine the resultant velocity of...
  33. N

    Average Speed vs. Instantaneous Speed

    Homework Statement A book falls off a shelf and lands on the floor. Which is greater, the book's average speed or its instantaneous speed right before it lands? Homework Equations v = d/t The Attempt at a Solution I think its the instantaneous speed because the book accelerates...
  34. S

    MHB Solving problems using the Average Value function

    The miles per gallon of my car on a recent trip at time t was given by $mpg(t) = 30 + 10sin(t)$ where $0 <= t <= \pi$. Find the average value of $mpg(t)$ over this time interval. So I'm kind of confused on how to do this. Here is what I have set up, let me know if I'm on the wrong track or not...
  35. G

    Average Velocity and Angle of Inclination of a Slope

    What is the relationship between a ball rolling down a slope (ramp) and its average velocity. I know we are supposed to use: v^2 = ut + at/2 and F = mgsin(degree). But assume initial velocity is zero. Also if I do an experiment and I get results (make a graph between average velocity and...
  36. Q

    Bad Question - Average Acceleration

    Homework Statement A car starts from rest. With constant acceleration, the car increases its speed from 10m/s to 50m/s over a distance of 60m. How long does this take? Purported answer: 4.0s Homework Equations Constant acceleration, so the following equations apply: Vf^2 = Vi^2...
  37. courtney101ann

    Calculating Average Net Force Exerted on a 15-g Bullet Fired from a Rifle

    A 15-g bullet is fired from a rifle. It takes 2.5 × 10^-3 s for the bullet to travel the length of the barrel, and it exits the barrel with a speed of 715 m/s . Assuming that the acceleration of the bullet is constant, find the average net force exerted on the bullet Answer : 4290 N I need...
  38. J

    Average velocity in two dimension with given functions?

    Suppose that the position vector for a particle is given as a function of time by vector r (t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct^2 + d, where a = 1.70 m/s, b = 1.05 m, c = 0.126 m/s2, and d = 1.12 m. So, I evaluated x(t) and y(t) at each time: x(t): 1.70*2.05+1.05 which...
  39. K

    Average shear stress in the glue joint between a spliced rod?

    Problem statement: Two 3/4-in.-diameter nylon rods are spliced together by gluing a 2-in. section of plastic pipe over the rod ends, as shown in the figure. If a tensile force of P = 500 lb is applied to the spliced nylon rod, what is the average shear stress in the glue going between the pipe...
  40. K

    Average shear stress in going between a spliced rod?

    Problem statement: Two 3/4-in.-diameter nylon rods are spliced together by gluing a 2-in. section of plastic pipe over the rod ends, as shown in the figure. If a tensile force of P = 500 lb is applied to the spliced nylon rod, what is the average shear stress in the glue going between the pipe...
  41. S

    MHB Use midpoint rule to estimate the average velocity?

    Use the midpoint rule to estimate the average velocity of the car during the first 12 seconds. Click here to see the graph from my book. i understand the midpoint rule is \frac{b - a}{n} so \frac{12}{4} = 3 so n = 3 I also know that \frac{1}{12} \int^{12}_{0} v(t)dt But now I'm...
  42. M

    What are the variables in the formula for average acceleration?

    The formula for average acceleration is (v_final - v_initial) / (t_initial - t_final), I was wondering if v_initial and _final are the instantaneous velocities (found by second derivative of a function) at those points or are they the average velocities (found by change in distance over time)...
  43. N

    Transforming a spatial average into a spectral average

    Hi, First off, apologies if this is in the wrong place - any directions on where this is more appropriate are appreciated. I am trying to figure out how to convert a smoothing operation in physical space into one in Fourier space. In physical space, with equally spaced points x_j, (j...
  44. Q

    Average Velocity: Find the Answer

    Homework Statement The coordinate of an object is given as a function of time by x = 7t - 3t^2, where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is? (1) -5 m/s (2) 5 m/s (3) 11 m/s (4) -11 m/s (5) -14.5 m/s Homework Equations Average...
  45. adjacent

    Understanding the Average: Finding the Middle Number

    Homework Statement Obviously this is not a homework question,but I put this here as this looks like one. Lets see. The average of something is \frac{Sum of all the numbers}{Amount of the numbers.} For example,1,2,3,4,5,6 The average is 3.5 which is also the middle of the sequence. If the...
  46. N

    Direction of car's average acceleration vector as it turns

    Homework Statement A car, initially going east ward, rounds a 90 degree curve and ends up heading southward. If the speedometer reading remains constant, what's the direction of the car's average acceleration. The Attempt at a Solution a = Δv/Δt vi = (c,0) vf = (0,-c) (vf -...
  47. U

    Average and variance of a unit sphere

    Homework Statement Consider the sphere x2 + y2 + z2 = 1 Find the mean and variance. Homework Equations The Attempt at a Solution Mean = 0 (Symmetry) Variance Probability = \frac {dV}{\frac{4}{3} \pi R^3} = \frac {4 \pi r^2 dr}{\frac{4}{3} \pi R^3} = 3 \frac {r^2}{R^3} dr Variance =...
  48. C

    Engineering Find the average power absorbed by a specific resistor in circuit

    Homework Statement http://imageshack.us/a/img850/788/yk72.jpg Find the average power absorbed by the 2Ω resistor in the circuit (pictured above) Homework Equations Average power = (1/2)(Imax)(Vmax)(cosø) x=rcosθ y=rsinθ current division, voltage division The Attempt...
  49. 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°...
  50. C

    Average power absorbed by resistor:

    Homework Statement http://imageshack.us/a/img4/5259/wn5b.jpg Find the average power absorbed by the resistor in the circuit if v1(t) = 10cos(377t + 60°)V and v2(t) = 20cos(377t + 120°)V Homework Equations average power = (1/2)Vmax*Imax*cosø x=rcosθ y=rsinθ mag = (r2 +...
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