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. M

    Average size of connected components in grid

    Start with an infinite 2d grid of cells, with each cell randomly colored black or white (50% chance). Now take the graph G whose nodes are the cells, and with an edge (A, B) if A and B are adjacent in the grid, and the same color. What is the average size of a connected component of G? Is it...
  2. I

    Average of a tensor composed of unit vectors

    Hello, I'm studying The Theory of Polymer Dynamics by Doi and Edwards and on page 98 there is a tensor, defined as a composition of two identical unit vectors pointing from the monomer n to the monomer m: \hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm} As far as I understood, the unit vectors...
  3. M

    Finding Average Force Applied On A Slope

    Hi all. I am marking GCSE paper that I did myself. There is 1 problem that I do not seems to understand. Please help me. Thank you very much. Homework Statement Daniel pulls a 3kg box up a slope from rest as shown (Attached) Given that the average friction of a slope is 2N and the speed at...
  4. R

    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...
  5. O

    Average distance to surface of sphere

    Homework Statement First, the problem, quoted verbatim: "Neutrons are created (by a nuclear reaction) inside a hollow sphere of radius R. The newly created neutrons are uniformly distributed over the spherical volume. Assuming that all directions are equally probable (isotropy), what is...
  6. T

    Average IQ of professional physicists/mathematicians?

    Many scientists have never taken IQ tests so there is a lack of statistical data, but what is a realistic estimate? Do you think 135-140 would be the average?
  7. N

    Difference quotient problem and average rate of change

    Homework Statement A soccer ball is kicked into the air from a platform. The height of the ball, in metres, t seconds after it is kicked is modeled by h(t) = -4.9t^2 + 13.5t + 1.2. I solved for the expression that represents the average rate of change of height over the interval 2<= t <=...
  8. S

    Average power given velocity, kinetic friction, and mass

    A 23.5-kg rock is sliding on a rough, horizontal surface at 9.15 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.180. What average power is produced by friction as the rock stops? I think that the way to solve it is use...
  9. A

    Computing Average Age of Mothers in Age-Structured Population

    Hi, I have the following problem. Consider an age-structured population growing according to a Leslie matrix. Suppose the population is in stable exponential growth, i.e. its age-structure is constant in time, while the total population is exponentially growing (or decreasing) with exponent...
  10. somasimple

    Average distance of ions in solute?

    Hi, If we know the concentration of a salt (i.e NaCl) in a solute (i.e 0.1 M), is it possible to compute an average distance (in nm) of each Na vs/ Cl ions in this solute assumed mixed?
  11. S

    (Negative Average Velocity) Homework

    Thank you for helping! I got it :)
  12. S

    Confused with this negative average velocity

    EDIT ADDED: I already got it! Thank you for your ideas! :D 1. Homework Statement If you drive an average velocity of -72.8 Km/h for 55 minutes to a position that is 28.5 KM north of Jollitown, in what position did you start your drive?I'm confused with this negative average velocity, please...
  13. S

    What is the average day of an Engineer?

    I am interested in going into engineering. I enjoy literally using the scientific method to solve my problems in my life, I also have a knack for creativity and enjoy doing things efficiently. My problem is that, I still do not have an appropriate level of understanding or conception of...
  14. A

    Calculate the average force acting on the block

    Homework Statement A block of mass 2 kg starts from rest and begins to move at time t=0 along a straight line on a smooth horizontal surface. The displacement of the block, s, depends on time, t, given by s=3+2t+t^3 . t is expressed in second and s in meter. Calculate the average force acting...
  15. S

    Is there an analytical way to get average energy of a Fermi-Dirac gas?

    The average particle energy of a Fermi-Dirac gas, with zero chemical potential, is about 3.15T, where T is the temperture of this gas. To get the average energy, one needs to do an integration. The integrand is something like \frac{x^3}{e^{x/k_BT}+1}. I could get the result numerically. But...
  16. D

    Average relative velocity in calculating mean free path

    Hello, Does anyone know why we use the root mean square of the relative velocity in calculating the mean free path? As is done in this example: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/MolecularCollisions.htm Seems like it would make more sense to find the mean of the...
  17. J

    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)...
  18. A

    Average power to ZL coupling coefficent and mutual inductance M?

    Homework Statement In the circuit of Figure 4-2, let N1=2000 turns, N2=1000 turns, R=0, Z1=0 and ZL=300+j400 (Ω). If V1(max)=1500 V, what is the average power delivered to ZL? A. 5400 W B. 2700 W C. 337.5 W D. 675 WHomework Equations V2=(N2/N1)V1The Attempt at a Solution since turn factor is...
  19. C

    Engineering AC Circuit; find average and reactive power to load (and load V and I)

    Homework Statement In the circuit shown, a load having an impedance of 39 + j26Ω is fed from a voltage source through a line having an impedance of 1 + j4Ω. The rms value of the source voltage is 250V. a) Calculate the load current IL and voltage VL b) Calculate the average and reactive...
  20. R

    MHB Concave Downward Function and Average

    Please show that if f is a continuous concave downward function on [a,b],then the average of the function f is greater than f[(a+b)/2],thank you in advance.
  21. N

    Which Matters More for Optical Components: Average Power or Peak Power?

    Something that i have wondered for a long time is when an optical components power handling capability is discussed, is it the average power or peak power that is in question? Thanks.
  22. L

    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...
  23. B

    Using fourier transform to find moving average

    can you use Fourier transform to find a moving average on a data set? so, you do a Fourier transform on your one dimensional data set. next remove high order harmonics from FT result. do reverse Fourier transform on new FT result. And, vola! smoothed out data set.
  24. O

    Average distance between random points in 2D

    I'm looking for an analytical solution to a very simple problem I've come across. Start with a circle of radius a. Now place n points at random positions inside this circle. Can you calculate the expectation value for the mean distance between the points? For the sake of argument can you...
  25. P

    Calculating average power using impedance and rms current

    Homework Statement Calculate the average power (P) absorbed by the load shown below when its impedance is 56 +j15 ohms 21 A rms? Answer to three significant figures Homework Equations P=Irms^2*RThe Attempt at a Solution Converting 56 +j15 to polar form yields 57.9741 ohms @ 14.9951 degrees...
  26. L

    What is the average lifetime of a Muon in the laboratory frame?

    Consider a beam of positive Muons, of energy 0.3GeV in the laboratory. (i) What is the apparent mean lifetime of the Muon as measured in the laboratory frame? (ii) What is the mean distanced traveled by the Muon in the laboratory? I first tried using the E = pc and working out speed...
  27. X

    Average speed of person walking problem

    Homework Statement A person walks first at a constant speed 5m/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 3m/s. (a) What is her average speed over the entire trip? (b) Her average velocity over the entire trip? Homework...
  28. Saitama

    Calculating Average Force on Walls from Bouncing Ball Collisions

    Homework Statement A ball of mass m bounces between two parallel walls, such that its velocity v is perpendicular to the walls.The collisions with the walls are totally elastic. What is the average force exerted by the ball on the walls, if the distance between the walls is d? Homework...
  29. F

    Average acceleration from average velocity?

    Homework Statement A particle travels from point A to point B following a semicircular path (a half-circle) of radius 5 m, and it travels at a constant speed of 1 m/s. Find the average acceleration of the particle. Homework Equations Average acceleration = change in velocity/ change...
  30. E

    The average of a random process

    Hello all, I have the following continuous-time random process: v(t)=\sum_{k=0}^{K-1}\alpha_k(t)d_k+w(t) where d_k are i.i.d. random variables with zero mean and variance 1, alpha_k(t) is given, and w(t) is additive white Gaussian process of zero-mean and variance N_0. Can we say...
  31. B

    A problem when calculating the average of an array (c programming )?

    hi , I need to do the following Write a program that asks the user to enter a number. Then create an array of this size. Fill the array with random numbers between 0 and 10. Calculate the average value. I did the program but there is a problem in calculating the average . can some one tell me...
  32. shounakbhatta

    Average kinetic energy of molecules

    Hello, The formula for average kinetic energy of molecule is: k=3/2KT. Can anyone please explain the derivation without using calculus? Thanks, -- Shounak
  33. D

    Average cost of master and PhD programs in the US

    Hi All, The other day an old high school buddy of mine emailed me asking if I could find out about the general cost of master and PhD programs in math across American schools. I grew up in one of those 'stan countries', but have been living in the US for 7 years now. He's still there and as far...
  34. T

    Find average acceleration from two given velocities each at a given ti

    The velocity of an object at t=0 seconds is 40 m/s directed due North. The velocity of the same object at t=5 seconds is 30 m/s directed due east. Find the magnitude of the average acceleration of the object over the time interval from t=0 to t=5 seconds. Also, show the direction of the...
  35. S

    Inelastic Collision and average force between 2 trains

    I solved the question , but i need to check it with you guys ... I believe there is something wrong with part b . Homework Statement The 15000kg train A is running at 1.5 m/s on the horizontal tack (to the right) when it encounters a 12000kg train B running at 0.75m/s toward it (to the...
  36. N

    Determine max notmal stress, average shearing stress and bearing stres

    Homework Statement The position of piston Cd is locked and force P = 350lb is applied as shown. The diameter of all pins and bolts is 3/8 in., member BCE has a thickness of 1/4 in., and member Ef has a width of 1 in. adn thickness 1/4 in. Homework Equations The Attempt at a...
  37. C

    What is the Average Speed of a Car on a 100 Minute Trip?

    Homework Statement A car travels at a speed v (km/h) for 40 minutes, then at a speed v/2 for 40 minutes, and finally at a speed v/3 for 20 minutes. What is the average speed for the trip Homework Equations avg v = displacement / time The Attempt at a Solution 40v + 20v + 20/3 v...
  38. A

    Average power of a signal in spectral display

    Hello, I've got a modulated signal - Y(f) (the question doesn't say if AM or DSB or whatever) which it's spectral modulted signal is shown(in the file I've uploaded).its is modulated by a carrier of sum of several COS. It asks what is the average energy or power( I should decide) of the...
  39. A

    Derive average rate of change formula of cos

    Q. Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function: (cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h) A. cos(x+h) = cosxcosh - sinxsinh subtitute this to...
  40. H

    Help with an Average Acceleration question during a time period

    If a rugby player is running at 3.69 m/s and then decides to sprint in a straight line for a ball and 3.27 seconds later is running at 7.29 m/s, what is their average acceleration during that time? Units and direction of travel are not required Homework Equations The Attempt at a...
  41. J

    Find the average power delivered by the voltage source

    Homework Statement Homework Equations P = 1/2 Vm*Im*cos(θv - θi) The Attempt at a Solution First I added all the impedance values to find the total impedance seen by the source. Zt = j10 + (50 || 20 + j10) = 15 +j5 Ω Now since the circuit is not purely resistive, I can't...
  42. S

    Average acceleration given velocity points?

    How do you find average acceleration given a table with points of velocity (ft/sec)? t (sec): 0 15 30 45 60 v(t) (ft/sec):0 40 60 70 75 the question asks: Find the average acceleration of Rocket A over t=[0,60] seconds. I used change in v(t)/change in time to find 4...
  43. M

    Average Acceleration of a golf swing

    Hello, I'm actually working on a project, which record the acceleration of a golf club via an accelerometer. And with the data of it i have manage to draw a graphic of a golf swing. My question is : how can i get the average speed of the recorded data. Indication, the time is in ms.
  44. E

    Ambiguity in forumlas for average speed & average velocity

    I'm going to start with an example: On her way to school, a child discovered that her loonie is missing and there is a hole in her pocket. She turned back and walked 24 m east along the sidewalk. Then, she stopped for 18 s and decided to head back to school. After walking 11 m west, she found...
  45. P

    Calculating Average of 3 Ball Numbers Drawn from Bag

    In a bag there are 30 identical balls numbered from 1 to 30. Choose one after the other three balls (without Off Reset). What is the average value of the sum of the numbers of three balls chosen? I am not sure on how i am going to solve this so i think that we will have a variable X where X1...
  46. Arsenic&Lace

    I'm an average physics student. Where to go from here?

    I would classify myself as an average second year student with middling grades (essentially a 3.55 both in major and cumulative). It seems to me that if you want to be a physicist of any kind, you need such monumental passion and focus that an average student perhaps should not even bother. I'm...
  47. N

    How to calculate average power in this case?

    Homework Statement A runner is rises up by 4.5 meters in 3.5 seconds, what average power must be consumed? Homework Equations P=w/t w=F.d The Attempt at a Solution p=4.5/3.5= 1.28 watt
  48. 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...
  49. 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.
  50. 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.)...
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