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

    Why Can a Sound Wave Not Travel Faster than the Average Molecule Speed?

    I am having trouble understanding the following passage in my physics textbook, particularly the bolded sentence: "The speed of sound in a gas is closely related to the rms speed of the molecules of that gas. In a sound wave, the disturbance is passed from one molecule to another by...
  2. jisbon

    Deriving the expression for average vertical force

    Here's what I have done: Let t1 be the time taken for the ball to reach the ground after the first bounce, and ux be the initial speed in the horizontal direction of ball. Also, let v be the speed after the bounce. For horizontal, $$\dfrac {4}{3}H=U_{x}t_{1} $$ For vertical, $$H=\dfrac...
  3. D

    Calculating the average linear speed of all points in a rotating sphere

    Is there a way to calculate the average linear speed of all points in the volume of a sphere rotating on a single axis? Since points closer to the axis of rotation and the poles move slower than points further out, would the average speed be a simple function of r/2 and pi? It would seem that...
  4. A

    I Meaning of each member being a unit vector

    Summary: Meaning of each member being a unit vector, and how the products of each tensor can be averaged. Hello! I am struggling with understanding the meaning of "each member is a unit vector": I can see that N would represent the number of samples, and the pointy bracket represents an...
  5. C

    How to find an average acceleration using an average velocity?

    I calculated the average velocity in a previous problem and got 1.146788991m/s over a time of 8.72s. I know I can’t use a_ave=(Vf-Vi)/(Tf-Ti) because I don’t know the final velocity and have no way to find it. Do I multiply average velocity by time?
  6. lemon__meringue

    What is time average of tension?

    Summary: My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the time average of the tension in the string of the pendulum larger or smaller than mg? By how much? My homework question asks: Consider a simple pendulum, undergoing small oscillations. Is the...
  7. S

    Speeding bullet, average force by post on bullet

    used a) change in momentum / time, time from from kinematics equation d = vi+vf/2 *t ... 0.1 = 300*t =3.33*10^-4 then 600/0.00333 = 1.8*10 ^5 how to proceed?
  8. Alexandra Fabiello

    Finding distance east given west dist., velocities, and average velocity

    6.44 km * 1000 = 6440 m/2.51 m/s = 2565.737052 s = west time av = (6440 m + - east distance)/(2565.737052 s + east time) 2565.737052 s + east time = total time 1.28 m/s * total time = (6440 m) - (0.495 m/s * east time) 1.28 m/s * (2565.737052 s + east time) = (6440 m) - (0.495 m/s * east...
  9. A

    A Average transverse momentum as a function of the longitudinal momentum

    Hello everybody! I am working on a code in which I need to study the dependence of ##<p_T>## vs ##p_L## (the average transverse momentum and the longitudinal momentum of a particle). I am looking for references, papers, books, etc. concerning this topic, but I have not been so lucky. My...
  10. L

    Average velocity and instantaneous velocity

  11. B

    MHB Average Rate Of Change Formula

    Is this the correct symbol to use for average rate of change: \overline{\triangle}=\dfrac{f(b)-f(a)}{b-a}
  12. S

    Chemistry Calculation of average molecular speed

    We can calculate the average speed using this formula: uavg=root(8PV/ΠnM) I plugged in the following values: P= pi*10 atm (bar is approximately equal to atm) V=8lts n=2mol M=32*10^-3kg/mol But it is giving wrong answer. Can you tell me what went wrong?
  13. J

    A Liouville's theorem and time evolution of ensemble average

    With the Liouville's theorem $$\frac{{d\rho }}{{dt}} = \frac{{\partial \rho }}{{\partial t}} + \sum\limits_{a = 1}^{3N} {(\frac{{\partial \rho }}{{\partial {p_a}}}\frac{{d{p_a}}}{{dt}} + \frac{{\partial \rho }}{{\partial {q_a}}}\frac{{d{q_a}}}{{dt}})} = 0$$ when we calculate the time evolution...
  14. D

    Instantaneous versus average velocity?

    I have a hard time understanding what this problem even means. So I can't even begin with it.
  15. J

    Average kinetic energy in 1 dimension according to the M-B Distribution

    Summary: Integrating the 1 dimensional MB Distribution in terms of translational kinetic energy up to infinity, does not yield ##\frac{1}{2}k_BT## as it should be. The format for the 3 dimensional Maxwell-Boltzmann Distribution is ##A\cdot e^{-\frac{E}{k_BT}} \cdot g(E)## in which ##A## can be...
  16. karush

    MHB 2.6 Calculate the average velocity of the car in different time interval

    OK I just had time to post and hopefully ok but still typos maybe the graph was done in Deimos wanted to try tikx but not sure about the polynomial trying to as many physics homework before classes start on Aug 26 Mahalo
  17. F

    MHB What is the average profit on producing and selling 40 items per day

    business has an average cost of AC(x)= 100x+2x/x and its average revene per day is AR(x)= 100x+3/x what is the average profit on producing and selling 40 items per day how many must we sell to get an average daily of $80?
  18. karush

    MHB 2.3.17 Find the average acceleration for this interval.

    2.3.17 At $t=5\, s$ an object is traveling at $5 \, m/s$. At $t=8\, s$ its velocity is $-1\, m/s$ (a) Find the average acceleration for this interval. $$a_{av}=\frac{v_2-v_1}{t_2-t_1}=\frac{\Delta v}{\Delta t}$$ So $$a_{av}=\frac{-1-5}{8-5}=\frac{-6}{3}=-2 \, m/s$$ book answer $-2\...
  19. Efeguleroglu

    Why RMS for the average voltage in AC current?

    We write rms formula as $$v_{rms}=\sqrt\frac{\int_a^b[f(x)]^2dx}{|b-a|}$$ I know if we take arithmetic mean average voltage will be 0. So we want all voltage values to be positive. Why don't we do that: $$V_{average}=\frac{\int_a^b\sqrt{[f(x)]^2}dx}{|b-a|}$$ That's first what I did...
  20. Nikhil Rajagopalan

    Relation between temperature and average translational kinetic energy.

    Dear Experts, I have read from various sources that the temperature of a gas is related to the "average translational kinetic energy" of a molecule of gas. When there are molecules that support motion other than translational ,which may also have rotational and vibrational motion, How does those...
  21. K

    Finding the average water mass flow rate in a water rocket

    Could anyone kindly kind me as to where this formula is derived from and how, because I searched and can't find it anywhere
  22. F

    Query about the time average of an AC power supply

    Hi there, I have a query about electric power in AC systems. I am Chilean, and over here the power supply is 220 V (rms) at 50 Hz. Some countries use voltages in the range 200-230, but others use 110 V or so, at frequencies of 60 Hz. There is no uniqueness, but all work. My question is...
  23. S

    MHB Using ratios to calculate weights in a weighted average (or not)

    As a 'non-mathematician' (somebody who sucks at maths) I've been enjoying reading up on a lot of the stuff that flew over my head in maths class many years ago. I've encountered some examples of weighted averages and I've been puzzling over how one might derive the weights in the following...
  24. alexmahone

    Average electric field over a spherical surface

    I'm sure the average is going to be an integral, but \displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a} gives me a scalar, not a vector.
  25. A

    B Spatial Average of squared functions

    If averaging of a function over a volume is defined as ##\frac{\int_v f(x,y,z,t) dv}{\int_v dv}##. Now if the average ##f^2(x,y,z,t)## is given 0 over a volume,then ##f(x,y,z,t)## has to be necessarily 0 in the volume domain??
  26. S

    Average speed of molecules in a Fermi gas

    My first most obvious attempt was to use the relation ##<\epsilon> = \frac{3}{5}\epsilon_F## and the formula for kinetic energy, but this doesn't give the right answer and I'm frankly not sure why that's the case. My other idea was to use the Fermi statistic ##f(\epsilon)## which in this case...
  27. mertcan

    I Auto Regressive Moving Average Model (ARMA) Ljung-Box Test

    Hi, according to ARMA model it is said that in order to check out white noise terms, Ljung-Box is applied involving sum of squared autocorrelations of errors with relevant lags. In short, sum of them is chi-square distribution but n-p-q degree of freedom when we have ARMA(p,0,q) model. My...
  28. Philip Koeck

    The average potential inside an electrically neutral solid

    If a solid (a few nm diameter) was placed in vacuum inside a grounded hollow sphere, but without touching the sphere (zero gravity), qualitatively what would the potential inside this solid be on average? In other words I don't want to look so closely that I see the potential wells of the...
  29. AncientOne99

    Average force and angle, collision problem

    Homework Statement [/B] Ball with a mass of 0.1 kg travels at a speed of 10 m /s to the boy. Boy kicks the ball with foot so that it bounces back at an angle of 30 degrees with respect to the horizontal floor. The ball falls back to the ground 20 meters from the boy. With what average force...
  30. P

    The average force needed to throw a baseball 90mph?

    Homework Statement The average force needed to throw a baseball 90mph. I tried to find the force at 90mph on release and 90mph at the plate and got two wildly different answers and it seems off that they vary soo much. Homework Equations · Velocity- 90 mph or 40.23 m/s measured at...
  31. J

    What is the magnitude of the average force?

    Homework Statement An athlete on a sled is moving with a speed of 3m/s across a pond with ice. If the total mass of the sled-athlete system is 95 kg, what magnitude of force is required to bring the sled to rest in 15 seconds? Homework Equations Force acting = change in momentum/time that...
  32. R

    Finding Average Normal Stress in Rod

    Homework Statement Here's a snapshot of the problem: Homework Equations + Newton's 2nd Law. The Attempt at a Solution My question is: why does the delta P term have only a single 40 kN force considered, whereas for delta EF there's an F/2? Thanks for your time.
  33. W

    MHB Advanced Functions Average vs. Instantaneous velocity

    What do the average velocities on the very short time intervals [2,2.01] and [1.99,2] approximate? What relationship does this suggest exist between a velocity on an interval [a,b] and a velocity near t=a+b/2 for this type of polynomial?
  34. JD_PM

    Average electric field over a spherical surface

    Homework Statement I was working out problem 4, chapter 3 of Introduction to Electrodynamics by Griffiths: a) Show that the average electric field over a spherical surface, due to charges outside the sphere, is the same as the field at the centre. b) What is the average due to charges inside...
  35. D

    MHB Solving Math Problem: Average Distance from Earth to Proxima Centauri

    Hi, my name is Eddy and this is my first post on the forum. I like math but do not know a lot of it. I am hoping to find some help and guidance her on how to solve things i don't find an answer to online. This is the problem at hand The average distance from Earth to Moon is about 384,403 kms...
  36. S

    I Finding a Factor's Contribution to An Average of a Product

    Say that there is an object X = <ABC> = (A_1B_1C_1+A_2B_2C_2+...+A_NB_NC_N)/N Is there any way to say what X_A is? Or what exactly the A term in all of these terms contributed to X? Or is that info pretty much washed out in this type of ensemble average? Oh, and A, B and C are random...
  37. SamRoss

    Where can I find historic daily average temperatures?

    I am a middle school teacher who is very concerned about global warming. My students’ memories don’t go back very far and they think it is perfectly normal to see mild weather and little to no snow throughout the winter months in New York City. I would like to compare current temperatures each...
  38. JD_PM

    How to compute a mean square average

    Homework Statement We know that $$< (x_1 - x_2)^2 > = \frac{K_bT}{K}$$ $$< (x_2 - x_3)^2 > = \frac{K_bT}{\gamma}$$ What's ##< (x_3 - x_1)^2 >## equal to? Homework EquationsThe Attempt at a Solution I have tried: ##< (x_2 - x_3)^2 > - < (x_1 - x_2)^2 >## but did not get ##< (x_3 - x_1)^2...
  39. TachyonLord

    Find the average force at distance x

    Homework Statement A “superball” of mass m bounces back and forth with speed v between two parallel walls, as shown. The walls are initially separated by distance l. Gravity is neglected and the collisions are perfectly elastic. If one surface is slowly moved toward the other with speed V...
  40. Adesh

    Schools Can an average student ever get good university?

    Hello everyone, I want to ask can an average student get admission in good universities? By average student I mean a student who is not gifted with some great abilities and doesn't have any powerful family background but just yearns to achieve higher education. By good universities I mean...
  41. kolleamm

    Average response time in a conversation?

    Is there any average time between responses in a simple conversation using speech (not text)? For example Bob : Hello 1sec gap Mike : Hey!
  42. A

    Average force during a ball's elastic bounce off of a plate

    Homework Statement [/B]Homework Equations For this problem I have calculated the average force as ∫ Fdt/ ∫dt And using a(acceleration)=2h(height)/t2 and calculating the numerator it comes out -2m(mass)h/t ,but what will be the limit of the intergral in that case ?? Of course the...
  43. Viona

    Average Velocity of gas molecules calculated with a Boltzmann distribution

    Hello What is the meaning of the average velocity of gas molecules calculated by Boltzmann distribution (in kinetic theory of gases)? Does all molecules have the same average velocity?
  44. R

    Average Pressure Radiation on Perfectly Absorbing Surface

    Homework Statement A light source radiates a sinusoidal electromagnetic wave uniformly in all directions. This wave exerts an average pressure p on a perfectly reflecting surface a distance R away from it. What average pressure (in terms of p) would this wave exert on a perfectly absorbing...
  45. K

    MHB Average "Hits" on exploding dice

    Hey folks, I've been using a really simplistic equation for this and I'd like to get an actual table/equation/and standard deviations if possible. Here are the rules. roll xd6s (six-sided dice) every die that rolls a 4 or greater is a "hit." 6s rolled count as a hit and then "explode," adding...
  46. CDL

    Mean Frequency and Frequency Spread of a Laser Pulse

    Homework Statement Laser probes are being used to examine the states of atoms and molecules at high temporal resolution. A laser operating at a wavelength of 400 nm produces a 1 femtosecond pulse. Compute the mean frequency and frequency spread, ∆ν, of this laser pulse. Homework Equations c =...
  47. J

    MHB Find the average or mean slope of the function on a interval

    Hello I have the exercise below: Consider the function f(x)=1−8x2 on the interval [−5,6]. Find the average or mean slope of the function on this interval, i.e. [f(6)-f(-5)]/[6-(-5)] according to the theorem of laGrange the slope in a continues function which is derivable in an interval...
  48. Alexanddros81

    Calculate average speed/acceleration for the given function

    Homework Statement Serway Physics Chapter 2 20. An object moves along the x-axis according to the equation ##x=3.00t^2 - 2.00t+3.00##, where x is in meters and t is in seconds. Determine (a) the average speed between t=2.00s and t=3.00s, (b) the instantaneous speed at t = 2.00s and at t=3.00s...
  49. M

    Calculate Avg Power Output for 75kg Person Walking 100ft in 3min

    Homework Statement Calculate average power output for a 75 kilogram person walking from ground level up stairs to a final height of 100 feet (then stops) in a time of 3 minutes Homework Equations P= work/ time or P=Fv The Attempt at a Solution I thought this was more of an energy problem...
  50. Alexanddros81

    A ball bounces off a brick wall, Find the average acceleration

    Homework Statement Serway Physics Section 2.4 Acceleration 14. A 50.0-g Super Ball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average...
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