# 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. ### I Regression line with zero slope and average as best prediction

Hello, I was considering some made up data ##(X,Y)## and a its best fit regression line. The outcome variable ##Y## is the number of likes and ##X## is the number of comments on a website. We have 100 data points which spread in such a way that the best fit line has zero slope. This implies...
2. ### Average thermal power produced

I'm curious as to why the average power is not negative in this scenario, since I thought the friction force is in the opposite direction of velocity. As far as I see friction force is the only acting force in the problem, but I may be wrong. I solved this by simply doing (Friction Force *...
3. ### Average power of an elevator

The answer in the book is 400w. It said that ##P_{av}=Fv_{av}cos(F,v)=mgv_{av}cos(F,v)=400##w and F is upward force that is applied by elevator. Should velocity of the elevator be constant? Because it said that we have F=mg.
4. ### I Average magnetic moment of atom in magnetic field ##B##

from the partition function - am trying to show that ##\langle \mu \rangle = \beta^{-1} (\partial \log Z / \partial B)## where ##Z## is the canonical partition function for one atom, i.e. ##Z = \sum_{m=-j}^{j} \mathrm{exp}(\mu_0 \beta B m)##, and ##\mu = \mu_0 m##. The average...
5. ### Average velocity of a particle

For this, The solution to (a)(i) is 0 ft/s. However I got -4 ft/s. The formula I used was, ##v_{avg} = \frac{s_f - s_i}{t_f - t_i}## ##v_{avg} = \frac{\frac{1}{2}t^2_f - 6t_f + 23 - \frac{1}{2}t^2_i - 6t_i + 23}{t_f - t_i}## ##v_{avg} = \frac{ \frac{1}{2}(t^2_f - t^2_i) - 6(t_f - t_i)}{t_f -...
6. ### Kinematics : Average velocity problem

The car covers half of the road with an average velocity of v, so the elapsed time is equal to: ##t_1=\frac {d/2} {v}=\frac {d} {2v}## And it covers 1/4 of the road with an average velocity of 2v, so the elapsed time is equal to: ##t_2=\frac {d/4} {2v}=\frac {d} {8v}## Then it covers 1/8 of the...
7. ### Average Kinetic Energy of Electron in the Conduction Band

Hello, I've seen in a few books on solid state physics that one can deduce an expression for average K.E.: $$<\:K.E.>\:=E_c+3/2\:k_B\:T$$ from the following: $$<\:K.E.>\:=\:\frac{\int \:\left(E-E_c\right)g\left(E\right)f\left(E\right)dE}{\int \:g\left(E\right)f\left(E\right)dE}$$ I can't...
8. ### Average distance between asteroids in the asteroid belt

What I did was find the total area of the space between the Kirkwood gaps and the area occupied by the asteroids (assuming they all had a 100m radius). I subtracted the two to get the area that is empty in that region. To find the average empty area between asteroids I divided this by the...
9. ### A Average temperature in a greenhouse

Hello everyone, since several weeks, no response from the other forums, I tried to compute a simple model for a greenhouse in a garden. First idea was to compute mass transfer, Navier-Stokes and heat equation all together but in my knowledge no analytical solution exists.I need to build a simple...
10. ### 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.
11. ### Average force when a bouncy ball collides with surface

What have mistakes/wrong assumption have I made in solving this question? I tried to solve the problem this way N.B. I assume that the j hat direction is up.
12. ### Difference between average position of electron and average separation

Hi, I asked this question elsewhere, but I didn't understand the answer. It seems to be easy to understand, but for some reason I'm really confuse. I'm not sure how to find the average position of an electron and the average separation of an electron and his proton in a hydrogen atom. To be...
13. ### Average Electric Field over a Spherical Surface

The picture above shows the integral that needs to be evaluated, and the associated picture ## \cos\alpha ## can be obtained via the law of cosines. I'm simply confused as to where the ##\cos\alpha ## comes from in the first place. I just don't see why ##\cos\alpha ## is necessary in this...
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### I Car low average speed vs aero drag relation

I drive car only at country roads allways at speeds 100-120km/h, no city and no idle time-heating engine etc. Why computer allways show very low average speed , 40-48km/h?I allways have feeling that this speed is too low because I allways drive way faster then this. Indeed all my friends have...
15. ### I Averages and average speed/instantaneous speed relation

Hello, Given a set of numbers, we can calculate their average and there are different types of averages (arithmetic, weighted, harmonic, geometric, etc.) The choice of the average depends on the situation. The average, also called mean or expectation value, is a number that can replace all the...

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### I Proof of average height of half circle

I need proof how find average height of half circle? Lets say pressure distribution is half circle with Pmax = radius,I must find average/resultant pressure..
30. ### Confused about calculating the average energy from a distribution graph

Hello, in one of tasks of my liquid scintillation lab is to determine the average energy. You can see from the graph that data I obtained is similar to this one that I have a excel sheet data. X-axis is for beta particle energy from 0-156keV while y-axis counts of the particles. So according to...
31. ### Magnitude and average value of energy intensity of light beam

I tried using the equations above, but I wasn't really able to come up with an intuitive explanation. From my understanding, the electric field vector only varies in the x-y plane while the magnetic field vector only varies in the z-y plane. Also, both vary sinusoidally and both reach extrema...
32. ### I Why we know average speed of single photon equal speed of EM wave?

Why we know that average speed of a single photon(in point particle view) equal the speed of EM wave?If average speed of a single photon smaller than c then there exist massive photons?
33. ### I Average field inside spherical shell of charge

A known result is that the average field inside a sphere due to all the charges inside the sphere itself is proportional to the dipole momentum of the charge distribution (see, for example, here). I wonder whether the same result can be applied in the case of a spherical shell of non-uniform...
34. ### I Experimental average lifetime of particles

My professor said that if I take 10^24 particles, for example, and I observe them for 1 years, I can say that their average lifetime is at least 10^24 years. I am not able to understand why, I though the law of decay is N(t) = N0*e^(-ta), so if after 1 year N(t) = N0, I can say ta ~ 0 , so tau...
35. ### Question about the average acceleration

Hello everyone, I have to find the average acceleration in the intervals 0m - 30m, 30m - 60m, and 60m - 90m. Here is the table: Position (m) 0 10 20 30 40 50 60 70 80 90 100 Time (s) 0 1,89 2,88 3,78 4,64 5,47 6,29 7,10 7,92 8,75 9,58 My teacher has given us the answers, but we have to...
36. ### Labwork Statistics help: Average of averages

I have done the experiment, and have a lot of data. For each data point (we have five), we did ten repetitions, for which we need to do video analysis. The analysis works frame by frame and gives a velocity between each frame. So, to get the value of one repetition, we already need to calculate...
37. ### I Looking for materials about ensemble average

Hello. I am looking for some materials related to the ensemble average. Specifically, suppose there is a function ##A(x)## satisfying a Gaussian white noise $$\left < A(x)A(x') \right > =A_0^2\exp \left ( -\frac 1 {L^2}(x-x')^2\right )$$ where the average is taken over an ensemble. Now I need...
38. ### I Van der Waals attractive force: Why don't the imbalances average out?

The summary refers, for example, to the Wikipedia explanation "The force results from a transient shift in electron density. Specifically, the electron density may temporarily shift more greatly to one side of the nucleus. This generates a transient charge to which a nearby atom can be either...
39. ### B Average Speed vs. Velocity: Explained

Though average speed over a finite interval of time is greater or equal to the magnitude of the average velocity, Instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant. Why so?
40. ### Average acceleration of an arrow by a bow

Distance= (Intial Velocity + Final Velocity / 2) Time 0.75 = (0+75 / 2) Time 0.75 = (37.5) Time 0.02 seconds = Time Acceleration = (Final Velocity + Intial Velocity) / Time Acceleration = (75 - 0) / 0.02 Acceleration = 3750 m/s2 Idk if this is correct can someone help pls.
41. ### Average acceleration of a car changing speed and direction

Nevermind I found what I had to do, thank you though.
42. ### B The average value of S operator

While reading in the book of Introduction to Quantum Mechanics by David Griffith in the section of Fine structure of Hydrogen: spin- orbit coupling, he said that the average value of S operator is considered to be the projection of S onto J. I could not understand why he assumed that. please...
43. ### I What is the average annual accumulation of cosmic dust on Earth?

By "accumulation", I mean depth at the Earth's surface (i.e., whatever volume it is would be divided up the surface area). This dust would be from anything (e.g., meteors, stardust, etc.), but would only count stuff that ends up as dust (i.e., no gas or liquid). I guess a follow-on question...
44. ### Question about the Peak and Average Power of a Laser

Hi, I am reading paper that I have to give a quick presentation on. I want to calculate the average power and peak power of the laser used, a Ti:Saphire laser. I have the wavelength they are lasing at (450nm), the repetition rate 81Mhz and the pulse duration (pulse width) of 100fs. I have done...
45. ### Admissions Having an A- average in upper division physics course

Hello, all I'm a rising senior who's about to apply for grad school. However, this year has been a rough year for me as my overall grade has declined a bit, especially in that I did not do well in 3 core major courses: mechanics B and EM II I got a B and STAT MECH B+(sadly, I thought i deserved...
46. ### Engineering Average heat transfer coefficient (forced convection)

So firstly, I don't understand if the mass flow rate is for steam or for water. If it is for water, I know I can find the heat transfer rate using equation:Q=mcdeltaT. But then I don't know how to find h (the average heat transfer coefficient) because I don't know the surface area (As). I can...
47. ### MHB How do I find the average of two averages?

In a statistical study, several measurements were taken and the average value of the measurements was 10.2. In a new survey, twice as many measurements were taken and the mean of these measurements was 10.8. What is the mean of all the measurements?
48. ### Time Average Value of Pendulum String Tension

Another member and I, in private conversations, have been discussing the time average tension in a pendulum string. He has done a numerical analysis of the problem, and his calculations indicate that the time average tension is less than mg. I have analyzed the problem analytically by...
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### MATLAB Average columns excluding nan

Hi PF! Given a matrix A = [1 2; nan 3; 3 4], how can I calculate the mean so that the resulting matrix averages the columns but ignores the nan values as non-entries, so that the mean of matrix A outputs [2,3]? Thanks so much!
50. ### How do I find average kinetic energy if I don't have mass of the gas?

So always in my problems i had mass (M) but now i don't and it seems impossible to solve this problem if I don't have mass I think i am missing something. I was looking for similar problems in my book and internet and didn't find any.