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. B

    Average force on a baseball when struck by a bat

    Homework Statement Baseball(0.145kg) pitch is pitched horizontally at 32m/s, ball pops straight up to a height of 36.5m. If the contact time between bat and ball is 2.5ms, calculate the average force between the ball and the batt during contact. Homework Equations Favg = Δp/t KE=KE The...
  2. C

    Average velocity or average values of functions and calculus

    Hi, I have some questions regarding values of function and average acceleration/velocity and really just want to make sure i am right :) if a function, let's say acceleration = 2 m/s^2 is a constant Then the average acceleration = (v2-v1)/(t2-t1) between two points is the slope of a straight...
  3. N

    Average speed question: forwards then backwards

    Homework Statement An object starts at the origin, position A; then travels 20 m to position B; then returns to position A. From A to B the average speed is 10 m/s; on its way back the average speed is 6 m/s. What is the average speed for the entire trip? Homework Equations average speed =...
  4. C

    Average velocity, me understand

    Hi, can someone explain to my how average velocity is in any way significant? Could it not just be avoided or ignored in physics? Here is why: If you travel 10 meters forward and 10 meters backwards the average velocity is zero so it tells you nothing about how fast you went, only in one...
  5. X

    Calculating Average Emission Wavelength from Spectral Intensity Chart

    I haven't had calculus in over 2 years and so I am not exactly sure how to go about this. I am inclined to believe some form of integration would be needed. I took the chart below from a paper on LED wavelength emission. The authors say that the vertical line represents the average emission...
  6. nviander

    What Speed Do You Need for the Rest of Your Trip to Average 2 m/s?

    Homework Statement In going to the store, you walk half of the distance at 1 m/s. At this point, you decide that you should pick up the pace. You would like to average 2 m/s for the entire trip. How fast must you move for the remainder of your trip in order to do so? Hint: the answer is not 3...
  7. Meadow_Lark

    When Does a Disc Reach Its Average Angular Velocity During Each Revolution?

    I am so confused by this question. I do not have a clue what I am supposed to do here. Can you please help?? [1pt] For each ith revolution, at what time point does the disc reach its average angular velocity? For example, for the 10th revolution what is the total elapsed time from the...
  8. P

    Calculating the average force of a molecule in a vessel

    Homework Statement Suppose an oxygen molecule traveling at the speed of 484 m/s bounces back and forth between opposite sides of a cubical vessel 0.1 m on a side. What is the average force the molecule exerts on one of the walls of the container? Homework Equations F=p/t The Attempt at a...
  9. G

    Expected Value and Auto Covariance for Moving Average Process with Lag h=s-t

    Homework Statement Y_t = u_(t-1) + u_(t) + u_(t+1) where u~WN(0,sigma^2) Find expected value, and auto covariance as a function of lag h = s-t for some s and t Homework EquationsThe Attempt at a Solution so E(y) = 0 cov(Y_t, Y_h) = cov(u_(t-1) + u_(t) + u_(s-t+1), u_(s-t-1) + u_(t) +...
  10. S

    Average velocity, displacement vector.

    Homework Statement Suppose that a car moves up north 100 km for 2 h and then turns towards east and travels in this direction 60 km for 1 h. a. Draw in the following diagram the displacement vector of the car? b. Determine the average velocity and the speed of the car. c. Answer the question...
  11. F

    Calculate average current flow in an electric eel (Simple Circuit Questions)

    Homework Statement i) A particular source of potential difference is capable of providing a maximum potential difference of 2 Volts. Sketch how you would connect two such sources to provide a potential difference of 4 Volts. ii) If each source can provide a current of 20 mA before its...
  12. A

    Find the net average power of a magnetic system

    Homework Statement We are given a circuit with a inductor that has a magnetic core and a magnet that is moving away from the inductor and to the inductor. We can control the flow of current through the inductor using 4 switches. We have to find the net average power at the output of the battery...
  13. K

    Statistical mechanics, spin average

    This is an exercise from an old examination that I am trying to understand by following the given solution to this problem. The exercise is about to calculate the four spin average <SiSjSkSl> and the indices i,j,k and l, given a Hamiltonian H. Solution: The problem is that i can't follow the...
  14. F

    Calculating Average Distance Diffused

    Homework Statement In a simple model of diffusion in one dimension the quantity D can be shown to be given by half the product of the mean free path and the rms speed of the diffusing particle. Calculate the average distance a molecule of insulin will diffuse in water in one hour if its...
  15. M

    Uncertainty in Average Intensity Calculation

    Homework Statement I am analysing intensities of some pictures. There are specific regions of higher intensities and so far i have managed to locate those regions automatically in Mathematica and the program returns the average intensity and standard deviation on this regions ("circles"), so I...
  16. T

    Average displacement based on probability .

    I am just curious, if I happen to get average value of displacement x = 0 (as in <x> = 0), does it mean it is zero because there are equal chances of being right or left of the initial position (assuming a point moves horizontally only, to right or left of the initial postion = 0)? Then, even if...
  17. Whovian

    Apparent indiscrepancy in the average value of phi function

    So, while solving a problem a friend came up with involving the Totient function, I ended up doing a bit of research into the average asymptotics of the function. On page 268 of Introduction to the Theory of Numbers, it's mentioned that "The average of order of ##\phi\left(n\right)## is...
  18. STEMucator

    What Are the Average and RMS Values of Waveforms?

    Homework Statement I had two small questions about the following problems. 1. Find the average and RMS values of the following waveform: 2. Show that the average and RMS values of the following sawtooth are independent of the position of the peak and are given by ##0.5## and ##0.577## of...
  19. Prashasti

    Why Is Power Factor Not Included in Series LCR Circuit Calculations?

    Hello! Homework Statement A sinusoidal voltage of peak 283 V and frequency 50 Hz is applied to a series LCR circuit in when R = 3ohm, L is 25.48mH and C is 796 microF. Find the power dissipated in the circuit. The book says, Power = I^2 R Where I = rms current. Now, I = 283/5 \sqrt{2} =...
  20. L

    Kinematic Equations Used to Find A.) Average Speed & B.)Acceleration

    Homework Statement A truck covers 40.0m in 7.15 s while uniformly slowing down to a final velocity of 3.50 m/s. a.) Find the truck's original speed b.) Find it's acceleration Homework Equations Δx = Vav(Δt) = (V+Vo/2)Δt a=(V-Vo)/(Δt) The Attempt at a Solution Part A.)...
  21. J

    Questioning the GDP Deflator: Measuring Average Price Output?

    I would like to raise a question about GDP deflator. In my macroeconomics textbook, there is a statement like this: "GDP deflator gives the average price of output". I wonder why the deflator will give the average price as it only measure the ratio between nominal GDP and real GDP... Thanks for...
  22. A

    Average of any operator with Hamiltonian

    Homework Statement Prove that for any stationary state the average of the commutator of any operator with the Hamiltonian is zero: \langle\left[\hat{A},\hat{H}\right]\rangle = 0. Substitute for \hat{A} the (virial) operator:\hat{A} = \frac{1}{2}\sum\limits_i\left(\hat{p}_ix_i...
  23. T

    Calculating average energy of a system with 3 energy levels

    Homework Statement A system has three energy levels, E1=0, E2 =1 and E3 = 2. In a certain state of the system, the probability that energy level 1 is occupied is 0.1, that energy level 2 is occupied is 0.8, and that energy level 3 is occupied is 0.1. Is this an equilibrium or a non-equilibrium...
  24. S

    Is Average Speed a Scalar quantity?

    Is Average Speed a Scalar quantity?
  25. Y

    What is its average speed during this 37 s interval? Answer in units o

    What is the magnitude of the instantaneous velocity (speed) of a freely falling object 37 s after it is released from a position of rest? Consider the acceleration of gravity to be 10 m/s2 . Answer in units of m/s What is its average speed during this 37 s interval? Answer in units of m/s
  26. C

    Average Speed between two cities

    Pauline travels between two cities. First she drives for 31 minutes at an average speed of 82 km/hr then for 23 minutes at an average speed of 51 km/hr, then she spends 25 minutes eating lunch and buying gas, and then she drives for 15 minutes at an average speed of 44 km/hr. Find Pauline’s...
  27. A

    Average value and probability density

    Homework Statement Consider a particle oscillating according to x(t) = a\cos(\omega t): Find \rho(x), the probability density to find particle at position x. Compute \langle x\rangle, \langle x^2\rangle. Homework Equations So in general we know that \textrm{Prob} = \int f_X...
  28. P

    Displacement, Average Speed, and Average Velocity

    Okay so I don't understand how to do the displacement of distance and time on a graph. I also need help with figuring out the average speed and average velocity. The graph deals with a Turtle's journey. On the Y-axis of the graph is distance in meters and the x-axis is time in minutes. The...
  29. END

    Vectors: Average Velocity, Acceleration, Speed

    Homework Statement A car is moving with speed ##17.4m/s## due south at one moment and ##28.3m/s## due east ##7.50s## later. A. Determine the magnitude and direction of its average velocity over this time interval. B. Determine the magnitude and direction of its average acceleration over...
  30. S

    How Do You Calculate Average Velocity for a Two-Part Journey?

    Homework Statement Starting from the front door of your ranch house, you walk 55.0m due east to your windmill, and then you turn around and slowly walk 40.0m west to a bench where you sit and watch the sunrise. It takes you 25.0s to walk from your house to the windmill and then 47.0s to walk...
  31. S

    Average kinetic energy of molecules of ideal gas

    I solved the problem myself immediately before anyone replied.
  32. B

    What is the average force exerted on a rocket during acceleration?

    Homework Statement A rocket with a mass of 7.2 x 10^4 kg starts from rest in outer space and fires its thrusters until it is moving with a velocity of 100 m/s. What was the average force on the rocket due to the thrusters? Homework Equations 1/2 mv^2 = Fxd The Attempt at a...
  33. V

    Diffusion -- What is average distance travelled?

    Homework Statement Would appreciate any help quite confused on this topic. If a type of ion has a diffusion coefficient of 10^-8 m^2/s in water. What is average distance traveled after 30 mins? What sort of graph should you plot in order to easily test validity of r=squarer root-2Dt. How...
  34. P

    Average of Multiple Stress Tensors

    I have a cluster of voxels and a 2nd order stress tensor corresponding to each voxel. I was wondering as to what would be the best method to calculate an average stress tensor for the cluster as a whole? Any constructive inputs would be greatly appreciated.
  35. J

    What does it mean when we say that average KE is equal to temperature?

    I know that delta h(Enthalpy) is heat and it is also the total kinetic energy of the system. Temperature is the average kinetic energy of the system from enthalpy. For example, a bathtub may have the same temperature as the ocean, but the total enthalpy will be greater for the ocean...
  36. S

    Why Is Average Velocity Calculated Differently in Various Scenarios?

    I'm trying to understand the kinematic equations well enough to explain to someone else, but the analogies I've come up with don't seem to be working well. 1) If a car travels 25 km/h for a certain distance, turns around in the opposite direction, and then turns back on its original path yet...
  37. WannabeNewton

    Average force between electric dipoles

    Homework Statement Consider a pair of electric dipoles ##\mu## and ##\mu'##, oriented in the directions ##(\theta,\phi)## and ##(\theta',\phi')## respectively; the distance ##R## between their centers is assumed to be fixed. The potential energy in this orientation is given by ##\varepsilon =...
  38. W

    Schools Getting into graduate school with average grades

    Hello all, I'm a German undergrad student wishing to do a physics graduate program in America. But the universities I looked at seems all too selective for me (for example at Louisiana State University they are looking for someone that have already done independent research and published...
  39. B

    What Is the Average Velocity of a Body Moving in a Circle with Constant Speed?

    Homework Statement I am just practicing and I found this problem: A Body is moving with constant speed v along a circle of radius R. Find the average velocity of the body from time t=0 to t = R/3V. Before I try to solve it, can you explain what it means? If speed v is constant, isn't average...
  40. B

    What is a valid assumption for modeling electrical systems as heat sources?

    Hi all, I've been looking for an answer to this for a while now but I can't explain to Google what I want to know. Hope I have better luck here. I'm an aerospace engineer working on a satellite project. In particular I'm currently working on the thermal analysis and I need to model up each of...
  41. A

    MHB Find Limit of (x^3/2 - 27)/(x-9) with Sample Values

    Hey guys, I would greatly appreciate some help for this question I'm working on at the moment: "1.a) Use the values 9.1, 9.01, 9.001, 9.0001 to guess at the value of lim x->9 (x^3/2 - 27)/(x-9) 1.b) Then, use appropriate factoring to find the limit of (a)" For part a, I took sample values...
  42. C

    Energy consumption for cooling and average temperature

    Good Morning, First, let me preface my question by stating that I do not have a background in physics so my question my or may not be ignorant. I simply have a curiosity and I am having trouble finding any results. My question is regarding air conditioners and cooling energy usage. Given...
  43. J

    Average value of a double integral over a region

    Homework Statement f(x,y) = ##e^{x+y}## D is the triangle vertices (0,0), (0,1) , (1,0) Homework Equations ##f(x,y)_{avg}=\frac{\iint_D f(x,y) dA}{\iint_D dA}## The Attempt at a Solution ##\iint_D dA \Rightarrow \int_{0}^{1}\int_{0}^{-y+1} dxdy = \frac{1}{2}## ##\iint_D...
  44. R

    Average of unweighted data

    I have some data from gas emission samples, part of the data was sampled in a region with a characteristic A and elsewhere with characteristic B. However, each region corresponds to a different percentage of total area. I want to calculate the central value (average or median) of unbalanced...
  45. F

    Which Average Velocity Formula Should I Use?

    Hey guys I just had a question regarding the equation to calculate average velocity. The first equation I've seen is: Vf+Vi/2, with Vf representing final velocity and Vi representing initial velocity. The second equation I've seen is Xf-Xi/Δt, with X representing position and Δt representing the...
  46. A

    MHB Average Value Theorem, Limits, and Slopes.

    Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: So for the first one, I just used f(b)-f(a)/ b-a and got 589, 1208, and 1366 respectively via simple substitution. For 1b, I...
  47. S

    Why does a light blinking quickly average out as 'on' to us?

    Consider a light, an L.E.D for example, turning on and off once per second. For humans, we will look at it and think "clearly on, clearly off, clearly on, clearly off" for each 'state'. Our view of whether it is on or off will continue like this if its 'blink frequency' is increased up to a...
  48. K

    Conceptual issue with average acceleration problem in Giancoli

    Hi all, I recently came upon the following problem in Giancoli's Physics Principles With Applications, 6th ed. textbook that I am having some issues understanding. I am new here, so I do apologize if I have made any mistakes in formatting or anything else. Homework Statement A 0.140-kg...
  49. B

    Calculating the Average Force on a Meteor Upon Entering Jupiter's Atmosphere

    Homework Statement A meteor with a mass of 1 kg moving at 20 km/s collides with Jupiter's atmosphere. The meteor penetrates 100 km into the atmosphere and disintegrates. What is the average force on the meteor once it enters Jupiter's atmosphere? (Note: ignore gravity). Homework...
  50. L

    Weighted average of a set of slopes with different goodness of fit

    Hi there, I have a bit of a confusing question, but I'll try to be as clear as I can in asking it. I have a set of linear fits for four different sets of data. Basically, I have three sets of data, with sample sizes N1 = 5, N2 = 7, N3 = 5 respectively. I have plotted these data with...
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