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. Domuks

    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.
  2. R

    Why don't we use the antiderivative factor for Average Voltage

    Below is the really quick derivation for average voltage. However when we do the anti-derivative a factor of ##1/\omega## should come out and the full answer should be ##\frac{2V_p}{\pi \omega}##. So why don't we include that? What's going on?
  3. L

    MHB Graph: showing that diameter is greater than average pairwise distance

    I need to prove the above statement. I have a very strong gut feeling that the above equation is not true, and so I need to find a case where the graph diameter is greater than the average pairwise distance. First off, I would like to clarify about the average pairwise distance, which is given...
  4. agnimusayoti

    Verify the average value of (1/r) for a 1s electron in the Hydrogen atom

    For spherical coordinate, ##dV = r^{2} \sin {\theta} dr d\theta d\phi## Therefore, $$<\frac{1}{r}> = \frac{1}{(\pi)(a_0)^{3}} \int_{0}^{\infty} {r e^{\frac{-2r}{a_0}} dr \int_0^{\pi} \sin {\theta}} d\theta \int_0^{2\pi} d\phi$$ From partial integral, I've found: $$\int_{0}^{\infty} r...
  5. Stonestreecty

    How to add up analogue inputs to average them?

    Hi, I would like to read a sensor (acs712) a number of times (20), add them all up, then divide them by the number of reads. So I can get an average. to give me a sort of analogue "debounce". Am I guessing the sum function? I sincerely appreciate any advice you can all give me, I'm incredibly...
  6. E

    Average Energy density and the Poynting vector of an EM wave

    Hi, In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as using the formula I don't really understand how to do...
  7. PhysicsTest

    Calculating Average Power and Energy Consumption for a Heater

    The v(t) = 120##\sqrt(2)\sin(2\pi 60t)##. Let the resistance of the heater be "R", then the rated power = 1500W. The rated power is the average power 1500 = ##\frac{120^2 *5 * 60} {12*60 * R} ## ->eq1 R = 4 Ohm. a. Instantaneous power is ##P = \frac{v^2} R ## -> eq2 ##P =...
  8. L

    Alternating current and Average power

    For a current i(t)=I_0\sin(\omega t+\varphi_0) period is ##T=\frac{2\pi}{\omega}##, Power is defined as p(t)=Ri^2(t). So period of power is not any more ##T=\frac{2\pi}{\omega}##. Why then average power is P=\frac{1}{T}\int^T_0p(t)d t. Why are we using the period of current and not of the...
  9. diegzumillo

    I Average of prime factors growth

    Hi there, bored physicist here. I wondered about factorization so I made some plots and a model fit to satiate my curiosity, but it only made me more curious. Now I just want the answers! I didn't know which prefix to use. "Hobbyist" seemed more appropriate but we don't have that so I went with...
  10. M

    MHB Solve Computing an Average Problem | Help

    I can't seem to understand how to solve this problem. Please help
  11. TheBigDig

    Average of 3 normally distributed random samples

    I've found part (i) by calculating the z-score for 40 $$Z = \frac {40- 50} {15} = -0.67$$ $$N(-0.67) = 1- N(0.67) $$ $$1- N(0.67) = 1-0.7486 = 0.2514$$ But parts (ii) and (iii) are confusing me. I have answers provided by my professor that say the mean and std deviation for (ii) and (iii) are...
  12. icesalmon

    Engineering Find the Average Power absorbed by the 20k Resistor

    I wrote the following equations using node voltage, my issue is that I'm confused about why the RC branch at the output doesn't effect the value of the Gain for the amplifier; the equation involving VA / ( 20k - j12k ) is omitted in the solution. IAC = IAB + IBC V- = V+ = VB = VS ( VA-VC...
  13. T

    Average Kinetic Energy of molecules calculation

    the answer in the solution book is 29K which only comes if I use mass for only one atom. ( They did not show any working ) My attempt: 1/2 x (1.67 x 10^(-27)) x (355)^(2) = 3/2 x 1.38 x 10^(-23) x T T = 29.48820652 K The confusion arises when I tried the following question: Q. Estimate the...
  14. O

    How to find d2 when given d1 and d, total time, and average velocity?

    I rearranged the displacement formula to d2 = d + d1. I used cosine law to solve for d2 since the triangle is not right-angled but I am not getting the correct answer or angle for d2. The angle I used in cosine law (based on the diagram) was 32+12+90 = 134. d = v(t) = 130(3) = 390 km/h [N 32 E]...
  15. arcTomato

    A Average of the power spectrum of Poisson noise

    I am learning about noise that follows a Poisson distribution. When I do a Fourier transform of the data with only Poisson noise to get the power spectrum, what is the average value of the power spectrum?
  16. N

    Question about world average temperatures 1880- early 20th century

    (Note: this is posted in the spirit of having a civil, science based discussion. I have found that whenever questions are asked concerning climate research, a lot of people get upset for no reason and try to shut down any discussion by using only arguments of appeal to authority (meaning the...
  17. aatari

    Find the Magnitude of Average velocity using the given vectors

    Hi Guys I've attempted the question but not sure if the approach I used is correct. Would someone please have a look at my solution and let me know if it makes sense. Thanks!
  18. greg_rack

    Average power used to stretch a spring

    First and foremost, I found the max stretch of the spring using the strain energy formula(x=√((2*0.25J)/k)) ). Then, the maximum force exerted(Fmax=k*xmax), in order to find out the seconds needed for the force in [N/s] to reach its maximum value. Now, I got confused about how to find the...
  19. gonadas91

    A Random potential disorder average

    Hi, I have a basic question concerning disorder average in random potentials. Suppose we have a hamiltonian (in second quantised notation) in the form: $$H=H_{0}+\int d\vec{r}\psi^{\dagger}(\vec{r})V(\vec{r})\psi(\vec{r})$$ with ##V(\vec{r})## some random potential satisfying ##\langle...
  20. mcastillo356

    Average speed (or maybe average velocity) of an athlete

    Hi PF It's a multiple choice exercise, and the answer is 10 m/s. I've been wondering why, but no way. Regards
  21. Sunny Singh

    Relaxation time and average electron velocity in Drude model

    If τ is the relaxation time, τ means, on average the time between two collisions for an electron moving under a constant electric field inside a metal. Now according to the assumptions of drude model, the electron acquires an additional velocity of \frac{-eEt}{m}where t is the time elapsed since...
  22. P

    Peak Power vs Average Power

    It is an example problem and i could understand the solution and the answers are ## R = \frac {V_{rms}^2} {P_{av} } = 9.6 \Omega## ##I_{rms} = \frac {P_{av}} {V_{rms}} = 12.5 A## ##p_{max} = VI = 2P_{av} = 3000 W## But main problem is the statement given by the author below the solution which...
  23. E

    Average velocity in a turbulent flow tube

    hi guys I'm really struggling to get the expression for average speed in turbulent flow The book explains absolutely nothing about how the integration is carried out, in addition to the fact that the logarithmic term becomes undefined when r = R what I did was carry out the integration up to...
  24. aspodkfpo

    Average speed with constant acceleration over a period of time

    Say that we have an instance where something falls down from a certain height with constant acceleration g. We know that the average speed with regards to the time period is less than (u+v)/2 since we spend less time at the higher speeds. How do we actually calculate the average speed over a...
  25. R

    Maxwell distributions and average, RMS, and most probable speeds

    What I know about a Maxwell distribution is that an area under the distribution on an interval gives the fraction of the molecules with speeds on that interval. My first question is what does Maxwell's distribution represent? It is given by the formula ##P(v) = 4\pi \left(\frac{M}{2\pi...
  26. Yashi234

    Max lifting capacity for an average human adult

    I have situation where i have drawn a concept with 1 sheet covering width of box for model. But now i need to draw up the manufacturing drawings and it needs to lifted and assembled by 2 people. So i need to know if person weighs 70 kg how much weight they can lift without using mechanical aid...
  27. tanaygupta2000

    Minimum average value of position

    After getting the values of ψ₀(x) and ψ₁(x), I put them in the expression of ϕ(x) to get: ϕ(x) = (mw/πℏ)^(1/4) * exp[-(mw/2ℏ)x^2] * [α + βx√(2mw/ℏ)] Now when attempting to find the value of <x> by ∫xϕ(x) dx, I am having trouble determining the limits, as I am getting nothing useful by...
  28. hairey94

    Average Translational Kinetic Energy: P & V Given

    If this question asked for internal energy, then it is a straightforward thing, just use the formula U = (3/2) nRT = (3/2) PV. But the question specifically asked for average translational kinetic energy which I'm stuck with the value of T to plug in into the formula as the question only give us...
  29. SchroedingersLion

    Lennard Jones Potential and the Average Distance Between Two Particles

    Greetings! Suppose I have 2 particles that interact via a Lennard Jones potential $$U(\mathbf{q}_{1}, \mathbf{q}_{2}) = 4 \epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right] $$ with interparticle distance ##r=|\mathbf{q}_{1} - \mathbf{q}_{2}|##. The...
  30. A

    Temperature is a measure of the average kinetic energy of a gas?

    Why do they say temperature is a measure of average kinetic energy how is this possible. how can we take it is it applicable for all types of gases?
  31. phun_physics

    I Derivation of Average Square Energy Fluctuation in a Canonical System

    The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...
  32. Franklie001

    The average rate of energy loss resulting from internal friction

    Summary:: Having the following dates:
  33. J

    MHB Find the average force required to hold the gun in position

    A gun fires 6 bullets per second into a target. The mass of each bullet is 3g & the speed of 500 m/s. Find the average force required to hold the gun in position.
  34. A

    I Average of the B-field over a volume and surface integrals

    Purcell says that taking the surface integral of the magnetic field ##\textbf{B}## over the surfaces ##S_{1}, S_{2}, S_{3},...## below is a good way of finding the average of the volume integral of ##\textbf{B}## in the neighborhood of these surfaces. More specifically, he says in page...
  35. G

    I Average Number of Coin Flips to Reach a certain Head-Tail Difference?

    Let's say you keep flipping a coin until the number of heads exceeds the number of tails by 6, or vice-versa. It is very important to consider the "vice-versa". I did some digital simulations and found that the average number of flips required is about 35.4. How can we derive this number using...
  36. K

    Average speed and average velocity

    So thing that confusses me, is what is the difference regarding the calculation of speed and velocity? In think I should use the formula I wrote above to find the average velocity, but I don't understand what the formula for average speed will be then. By the way, when using the formula above...
  37. M

    Engineering Parseval's Theorem - Average Power of the difference of functions

    Hi, So I have a quick conceptual question about Parseval's theorem in this application. In previous parts of this question, we have found the average powers of both f(t) and g(t) by integration and using the complex Fourier series respectively (not sure if this is relevant to my question)...
  38. naushaan

    Calculating average acceleration during a time interval

    Here's my calculations for (a) and (b)
  39. Z

    I Is the calculation related to average or probability?

    Hi, I am trying to understand the calculation in the following research paper: http://cramton.umd.edu/market-design/abdulkadiroglu-sonmez-house-allocation.pdf
  40. Sakyo107

    Finding the Average Acceleration

    Hello, so I am working on a projectile motion lab but I'm not sure what to do right now. Essentially, the lab consisted of my classmates and I using an air table to show that the vertical and horizontal components of projectile motion are independent. During one of our trials, we placed a puck...
  41. C

    B Average Daily Balance for 2 consecutive months

    What does the term "average daily balance for two consecutive months" mean? For example. Suppose the account has $1 from February 1 to March 30. And it suddenly has $1 million dollars for March 31. If the penalty is charged if it's below $5. Does the big amount entered in the March 31 makes the...
  42. K

    I What is the average value of a bounded periodic function over a period?

    Does it make sense to just talk about the average value of a function without specifying the range over which the average is taken? It seems a common occurrence in discussions of waves to just mention that the average value of the complex exponential ##e^{ix}## is zero. But it will be zero only...
  43. Alefan_

    Average current around a magnetic loop that changes its shape

    To find out what the induced loop current was i used the formula: V=R×I To find out what the value of V was i used the formula that links electromotive force (fem) to angular speed: Fem=ω×B×A The only thing that's missing is the loops area but considering that it's a semicircle and that the...
  44. A

    Volume average of mass function

    I want to express <m(x,y,z)> over a sphere of radius R in terms of $$<\rho(x,y,z)>$$ e.g $$<m>=\frac{\int_{sphere R}m(x,y,z)dv}{\int_{sphere}dv}$$ $$<m>=\frac{\int_{sphereR}(\int \rho(x,y,z)dv)dv}{\int_{sphere R}dv}$$
  45. C

    Average speed needed to flip a vehicle

    Car A hits Car B's passenger side at intersection (T Bone). Car B flips over sideways in the direction of the driver's side. The intersection is basically level. Car A is an Audi 5, roughly 3,900 lbs. Car B is a Lexus NX, roughly 4,000 lbs. Car B had recently stopped and was traveling...
  46. RyanRhino

    Calculate the average force used to drag a box up a ramp

    I first wrote down that 55% = Eout/Ein I also know that W = (Facos20)(4) and I substitute it into the first equation 55% = Eout/[(Facos20)(4)] But I'm missing two variables here. Did i forget something or is the question missing some information?
  47. S

    Calculating Average Linear Velocity: 1.66m/s to 1.73m/s

    First i need the average linear velocity 100L/min = 0.1m3/min 0.00167m3/sec Cross Sec Area = Pie r2 =pie(0.0175m)2 9.61x10-4 m2 0.0016m3/s / 9.61x10x-4m2 = 1.66m/s But my notes say this should be 1.73 m/s Once i have the average linear velocity i can calculate Re. Help appreciated
  48. S

    I Operator for the local average of a growing oscillating function

    First some background, then the actual question... Background: (a) Very simple example: if we take ##Asin(x+ϕ)+0.1##, the average is obviously 0.1, which we can express as the integral over one period of the sine function. (assume that we know the period, but don't know the phase or other...
  49. karush

    MHB 3.1.5 AP Calculus Exam average temperature

    309 average temperature $$\begin{array}{|c|c|c|c|c|c|c|} \hline t\,(minutes)&0&4&9&15&20\\ \hline W(t)\,(degrees Farrenheit)&55.0&57.1&61.8&67.9&71.0\\ \hline \end{array}$$ The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W. where...
  50. S

    Average speed of a probability density wave and wave packets

    Show that ##v_{av}=\frac{\hbar k_2 + \hbar k_1}{2m}## is equal to ##v_{av}=\frac{\omega_2 - \omega_1}{k_2-k_1}##. Which of the identities listed above (if any) would make the sign change between ##k_2## and ##k_1##? One can attain a "wave packet" by superposing two or more sinusoidal waves...
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