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. V

    Displacement & Average Velocity

    Homework Statement A car travels in a straight line at 40 km/hr for 1 h and 60 km/hr for 2 h. A) How far does it travel? B) Find the average velocity. Homework Equations Average velocity = Δx/Δt (change in distance/change in time) The Attempt at a Solution In solving for A, I...
  2. J

    Can you have a negative average velocity?

    I understand that it's possible to have a negative instantaneous velocity, but I'm wondering if it's possible to have an negative average velocity. For example, let's say you start heading north at a constant 10 mph for an hour. The second hour, you drive south (directly toward the starting...
  3. P

    Taking a mean average of two probabilities to predict an outcome?

    I hope this the right place to ask this question. I appologize if this is in the wrong place. I am not from a probability background. I have tried to search for an answer to my question, but I have not found it in any of the literature which I can understand. I'm not even sure exactly how to...
  4. P

    The Sun, on average, is 93 million miles from Earth. How many meters is this?

    The Sun, on average, is 93 million miles from Earth. How many meters is this? Express using powers of ten. Express your answer using two significant figures. Okay so: Okay so, 1 Meter = 1609.344 x 93 = 149668.992 1.5 x 10^5 (2 significant figures) When I put 1.5x10^5 in, it says 'The...
  5. A

    The Difference Between Equation Uniform Acceleration and Average elocity

    Homework Statement I was just wondering in what instances you would use the two equation belows, and what the difference is between them. Homework Equations average velocity: vave = Δx/Δt Uniform Acceleration: vave = (vi+ vf )/2 The Attempt at a Solution I'm...
  6. Spinnor

    Connecting N points pairwise in volume V, average density of lines?

    Say we take N random points in a volume V and connect the points pairwise with line-segments. I would like to estimate the number of segments that intersect some small volume v, and where N is large enough so that any small random sample volume v will have many intersections. Little volume v may...
  7. C

    How Do You Calculate Average Speed in a Mixed-Speed Relay?

    Homework Statement The cheetah can run as fast as 113 km/h, the falcon can fly as fast as 161 km/h, and the sailfish can swim as fast as 105 km/h. The three of them run a relay with each covering a distance L at maximum speed. What is the average speed of this relay team for the entire...
  8. D

    Average Acceleration Question for Bullet Through Board

    Homework Statement "A bullet is fired through a 5.0 cm thick board of some material. The bullet strikes the board with a speed of 200 m/s, and emerges out the other end at 100 m/s.Homework Equations a= (change in velocity)/(change in time) average velocity = .5(initial v + final v)The Attempt...
  9. G

    Averaging average velocities

    We were told to time the linear motion of 3 objects over a certain distance three times. Then we were to use those times to calculate the object's Vavg for each trial. Finally we were supposed to average these averages to get the overall Vavg for each object. My question is: Is this an...
  10. K

    Not your average car collision (very real life ) - no values supplied

    Not your average car collision (very "real life") - no values supplied Homework Statement Hi, I've been given an assignment on a theoretical car collision. However, it is very "real world" (we are given information regarding the condition of each car before and after [particularly the...
  11. U

    How to Average Graphs with Different Time Indices?

    I have 10 sets of data which I have to analyze. The data represents a change in voltage over time and I want to come up with an "average" curve to represent the 10 sets of data. The problem is that the time index for each data is different so I can't simply average the voltage. Is there any...
  12. S

    Finding the Average Acceleration

    Homework Statement Starting from rest, a subway train first accelerates to 25m/s and then begins to brake. Forty-eight seconds after starting, it is moving at 17 m/s. What is its average acceleration in this 48-s interval? Homework Equations 1. v=v0+at 2. x=x0+(1/2)(v0+v)t 3...
  13. M

    Average time taken to study before GRE

    Hey all, Directed towards those of you that have tried, finished or are trying to get into a (US) graduate program (physics, but not necessarily); how long before the test did you start studying. I know in the case of physics the test is mostly lower division knowledge, but I'm just curious...
  14. V

    Average electron distance (GRE practice problem)

    Homework Statement Question 26 of the physics GRE from the practice test available here: https://www.ets.org/gre/subject/about/content/physics/ The normalized ground state wave function of hydrogen is \psi_{100}=\frac{2}{(4\pi)^{1/2}a_0^{3/2}}e^{-r/a_0}, where a_0 is the Bohr radius. What is...
  15. I

    Average Randomness Thought experiment

    "Average Randomness" Thought experiment Please bear with my explanation, I am, by no means a Physicist. During a recent theoretical thought experiment, I thought of a strange factor that I feel I should let out before it becomes forgotten by the constant wave of thought experiments that flow...
  16. S

    Negative Work but Average Force positive in this situation?

    I just want to make sure I'm understanding negative work correctly. An example problem where there is a bullet with an initial velocity of x m/s and a final velocity of 0 m/s. It is stopped by a wood block and the question asks to determine the amount of work done on the bullet by the block. If...
  17. J

    Integral? Average Velocity of a Spinning Propeller

    I'm trying to find the average velocity of a spinning propeller. v(r) = RPM C(r) / t ; C(r) = 2πr; t=(1 min) v(r) = RPM 2πr / (1 min) I'm not quite sure what to do next. I need the answer in units of velocity, but if I integrate that last equation, I won't get units of velocity. My rough...
  18. C

    Average Acceleration and Velocity Question

    Homework Statement An object traveling at a constant velocity v0 experiences a constant acceleration in the same direction for a period of time t. Then, an acceleration of equal magnitude is experienced in the opposite direction of v0 for the same period of time t. What is the object's final...
  19. fluidistic

    Estimating the average time between collisions (electrons in Cu solid)

    Homework Statement The thermal conductivity of Cu at room temperature is 400 W/(mK). Use this value to determine the average time between collisions, \tau. Compare this value with the electrical conductivity.Homework Equations Not sure. I take T=300K for room temperature. From a book and with...
  20. S

    Formula for average current on a coil inside a solenoid

    Homework Statement A solenoid of length 20.0 cm is made of 5000 circular coils. It carries a steady current of 10.0 A. Near its center is places a very flat and small coil with a resistance of 2.50 Ω made of 100 circular loops, each with a radius of 3.00 mm. This small coil is oriented so that...
  21. G

    Why Does Average Speed Calculation Differ for Uphill and Downhill Travel?

    Homework Statement A Bus drives 1km up a hill in 5.0 minutes. It then drives down the hill in 4.0 minutes. For the bus, find a) the average speed up the hill b) the average speed down the hill c)the average speed for the whole trip d)why is the answer for c) not equal to (speed up the hill +...
  22. K

    Average salary for a new assistant professor in Mathematics.

    I really like Mathematics and wondering for the salary for a new assistant professor in the subject.
  23. C

    Probability Finding Binomial Average Problem

    Homework Statement In each batch of manufactured articles, the proportion of defective articles is p. From each batch, a random sample of nine is taken and each of the nine articles is examined. If one article is found to be defective, the batch is rejected; otherwise, it is accepted. If...
  24. J

    Financial contract 2 - Average annual return computed in two ways.

    First i calculate the the average annual return for the Dow jones industrial average over the last 22 years by using the first and last value. To continue writing my code i also need to calculate the average return between two days separated by one year for every day over the last 22 years...
  25. B

    Prove relationship between average and marginal value

    Consider a set of n numbers, and let their arithmetic mean be X. Suppose a new number Y, is added to the set. Prove that the mean of the new set, with (n+1) members, is between X and Y. I've been trying to prove this the past few minutes, but I think I'm at a dead end. It's a problem that...
  26. N

    Calculating Average Acceleration of 52g Super Ball

    A 52.0-g Super Ball traveling at 28.0 m/s bounces off a brick wall and rebounds at 16.5 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.60 ms, what is the magnitude of the average acceleration of the ball during this time interval? Im not really sure...
  27. K

    How to correctly average over multiple data sets

    Homework Statement In a particular Magneto-Optic Kerr Effect (MOKE) experiment I have taken data for 20 hysteresis loops in which Kerr Voltage is measured as a function of Applied Field. I wish to obtain an average curve. The problem is this; Even though the settings for each loop were...
  28. S

    Calculating the Average Angular Acceleration of a CD

    Homework Statement Unlike the older vinal records which rotated at a constant ω of 33.3 rotations per minute (rpm), compact disks vary their rotation speed during the playing period. A certain CD has a diameter of 12cm and a playing time of 79 minutes. When the music starts, the CD is rotating...
  29. M

    Finding Uncertainty of Average Values

    Let's I have three values, 3.30±0.1, 3.32±0.1, and 3.31±0.1. How would I find the uncertainty of the average of these values?
  30. K

    How much lb could an average person push?

    e.g. pushing a door with x-lbs of resistance, assuming a person is exerting force perpendicular to the door, 36" from hinge. What is that x-lbs (max) an average adult could pushing with ease? Thanks
  31. Y

    What is the average radius of a betatron vacuum chamber?

    My friend and I were discussing particle accelerators (betatrons to be exact) and we began to argue about the size of the core magnets and vacuum chamber. He said that an average torodial vacuum chamber is 0.5m. I have seen old photos of them and said that's more likely to be the diameter. I...
  32. T

    Help Finding Average Acceleration

    Homework Statement NASA operates a 2.2 second drop tower at the Glenn Research Center in Ohio, where experimental packages are dropped from the top of the tower. a) What is the drop distance of a 2.2 s tower? b) How fast are the experiments traveling when they hit the airbags at the bottom...
  33. P

    Race Car Driver's Average speed

    A race car driver must average 200.0 km/h over the course of a time trial lasting ten laps. If the first nine laps were done at 198.0 km/h , what average speed must be maintained for the last lap? Avg Speed=Distance traveled/Time 218 km/h, I averaged the first 9 laps at 198 and plugged the...
  34. M

    Integrating to find average value

    I have the function: f(x,y)= x*(y^2)*e^-((x^2+y^2)/4), with x and y from -3 to 3 I took the integral of this function and got 0 as my answer. I need to find the average value, which is 1/area multiplied by the double integral. Since the double integral is 0, would the average value also be...
  35. T

    Chemistry The average separation between H2O molecules in pure water

    Homework Statement I can't answer to that question, and I don't know how to. I have to calculate the average separation between H2O molecules in pure water. Homework Equations The diameter of the molecule is 0.29 nm I think we can use the bohr equation to resolve it? r = (ε0*h2)...
  36. S

    Find Average Power Given Mass and Velocity

    During 12 s an engine increases the speed of a 1.5×103-kg vehicle from 13 m/s to 27 m/s. Assuming no losses, what average power is the engine producing? P = W/t W=FΔx W=ΔKE ΔKE=mvf2-mfi2 I tried finding the change in kinetic energy to solve the problem, but it didn't work. I got 3.4E3...
  37. DocZaius

    Gaussian center not average value?

    I put this under statistics because of your knowledge of the Gaussian. I have run into an elementary problem. I was considering what the average value, <x>, is for a Gaussian with an x offset, and got results which don't make sense to me. First, it is obvious that for P1(x)=e^(-(x^2)) the...
  38. E

    How to calculate average velocity

    The velocity of a river varies parabolicly with V adjacent to the banks and max velocity d halfway betwee the banks. The flow of river is parallel to the bank. The width of the river is x. How do you calculate the average velocity?
  39. N

    About Ensemble Average for gas molecules(classical mechanics regime)

    I have some question about Ensemble Average. The macroscopic variable of fluid is average of microscopic variable of gas molecule. And if time average is same with spatial average I know as it called edgodic. My question is that if two different microscopic variables which have same...
  40. S

    Difference between an expectation value and an average

    Hi everyone, What is the difference between an expectation value and an average. I may have this wrong, but is it something along these lines: You perform a series of measurements on a given observable, such as momentum, and the average value of all these measurements is your expectation...
  41. P

    What type of molecule has the highest average speed in a room filled with gases?

    Homework Statement The gases in this room include oxygen (molar mass 32 g), nitrogen (28 g), water (18 g), and carbon dioxide (44 g). Which type of molecule has the highest average speed? A) O2 B) N2 C) H2O D) CO2 E) They have the same average speed. Homework Equations...
  42. L

    The Parity Operator: Find the average value of the parity.

    Homework Statement A particle of mass m moves in the potential energy V(x)= \frac{1}{2} mω2x2 . The ground-state wave function is \psi0(x)=(\frac{a}{π})1/4e-ax2/2 and the first excited-state wave function is \psi1(x)=(\frac{4a^3}{π})1/4e-ax2/2 where a = mω/\hbar What is the average value of...
  43. P

    Average Energy of Grand Canonical Ensemble

    Hello, The entropy of the Grand Canonical Ensemble (GCE) is: S = KB ln ZG + (\bar{E}/T) - μo\bar{N}/T Helmholtz function is: F = \bar{E} - TS = \bar{E} - TKB ln ZG - \bar{E} + μo\bar{N} = -TKB ln ZG + μo\bar{N} But \partialF/\partialT = -S (From thermodynamics). Then...
  44. S

    Schools Average GPA for Engineering Freshman in College?

    Hey, I attend Georgia Tech and I am completing my freshman year here. I am probably going to end up with a 3.1 - 3.3 GPA this year. I was wondering whether this is poor, average, or good. Keep in mind that my major is Electrical Engineering which is considered to be one of the hardest majors at...
  45. R

    Average Speed Of a and b where d and t is not given

    A body covers half its journey with a speed of a m/s and the other half with a speed of b m/s Calculate the average speed of the body during the whole journey
  46. M

    Natural selection: What do they mean by average individual?

    Natural selection: What do they mean by "average" individual? You know how they say stabilizing selection favors the "average" individual - i.e, it is centered around the mean? I have a question. How do they calculate this "mean"? I'm confused. All I know is that if pure-white rats mate...
  47. E

    Average Back EMF Induced in Coil in Loudspeaker

    Hi, I would appreciate any help with the following: The coil in a loudspeaker has an inductance of L = 112 microH. To produce a sound of frequency 40kHz, the current must oscillate between peak values of + and - 4.4 A in half a period. What average back emf is induced in the coil during this...
  48. M

    How do you find the average value of a function on a surface?

    Homework Statement find the average value of (1+4z)**3 on the surface ... Homework Equations The Attempt at a Solution All I really want to know is how to go about this? Is the average value on the surface just the surface integral over the area of (1+4z)**3?
  49. X

    Calculating Average Tangential Stress for Non-Uniform Rotating Disk

    Assumed a disk loaded with external pressure Po, internal Pressure Pi and rotating at the speed ω. I'm sure that average tangential stress for uniform thickness rotating disk can be calculated using equation below : σ avg = (PiRi/Ro-Ri) - (PoRo/Ro-Ri) + (ρω^2) / 3(Ro^2+RoRi+Ri^2) Ro = outer...
  50. G

    Calculating Average Force Exerted on Child Swing

    I was given this question in a practice assignment; A 31.0 kg child on a swing reaches a maximum height of 1.92 m above her rest position. Assuming no loss of energy: 1.At what point during the swing will she attain her maximum speed? 2.What will be her maximum speed through the...
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