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. S

    Average value for a function over its entire domain

    As we know , the average value of a function over is : i wanted to calculate the average value of a function over its entire domain ( e.g ) firstly, i divided the interval into 2 intervals & and calculated the F_avg for each ,,, is my way correct ? thanks !
  2. A

    Insect wing physics? Average force?

    Homework Statement A typical flying insect applies an average force equal to twice its weight during each downward stroke while hovering. Take the mass of the insect to be 10 g, and assume the wings move an average downward distance of 1.0 cm during each stroke Assuming 100 downward strokes...
  3. X

    Average of standard deviation makes sense?

    I've a set of tests, and for each test, they have different size. I'll show an example. Test1 size - Time(seconds) 100 - 10 100 - 23 100 - 17 200 - 37 200 - 42 200 - 47 300 - 53 300 - 53 300 - 53 For each test, I took the average. Average1 size - average 100 - 16...
  4. A

    Calculating Average Acceleration in Terms of g's for a Car Collision

    Homework Statement A car traveling at 85km/h strikes a tree. the front end of the car comoresses and the driver comes to rest after traveling 0.8m. Homework Equations a) What was the average acceleration of the driver during the collision? b) Express the answer in terms of g's ; where...
  5. M

    Finding the average slope of a parable

    Homework Statement A parable is f(x) = 0,01x2-2x+100 it beginswith the cut with the y-axis and ends when it cuts the x-axis. Questions : a) find the average slope of the parable. b) Find the place on the parable where the average slope is present. Homework Equations here i...
  6. B

    Finding Average Velocity of Entire Trip

    I have been solving these sort of problems, and they follow this basic paradigm: first, they will tell me I traveled a distance D at a velocity of A, then they traveled the same distance D at a velocity of B. Why can't I simply just simply perform the following computation: (A+B)/2. I have been...
  7. A

    Average Force using Newton's Laws of Motion

    Homework Statement A 89.6 kg man steps off a platform 4.52 m above the ground. He keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend, and, treated as a particle, he moves an additional 0.88 m before coming to rest. Treating our rigid...
  8. K

    Calculating average power of a set of data

    There are n people with masses mn . Each run up a given slope of height h in times tn. Gravitational accelartion, g, is constant. Now there are 2 ways to calculate the average power of this group of people with 2 different results. The question is which way of calculating the average power...
  9. teroenza

    Time average of SHO kinetic energy = (1/2)E

    Homework Statement I believe I understand the problem except I cannot get the time average of [sin(wt-d)]^2 = ½ I can do the rest once this is established. Homework Equations Average of a function= <function>= 1/(period)* integral(f*dt) from 0 to the period Function to be...
  10. G

    How do you find average value of normal acceleration?

    Homework Statement Find average value of Normal Acceleration from the information given. (See the picture) Homework Equations a^{→}_{ave}= Δv^{→}/Δt a_{t}=Δv/Δt The Attempt at a Solution I took the difference of the given angles in radians and divided it twice by Δt and get...
  11. A

    Wave Runup - Average Reservoir Depth

    Hello! In order to calculate wave run-up for a reservoir, I need to determine the average reservoir depth along fetch line (D).... Does anyone know how can I calculate this depth? In some book I have read that D is the average reservoir level along the direction of wind blow, and it is...
  12. S

    Average induced emf in coil with turns

    Homework Statement A closely wound rectangular coil of 95.0 turns has dimensions of 29.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 39.0 degrees with a magnetic field of 1.60 T to a position perpendicular to the field. The rotation takes 0.120 s...
  13. R

    Average Velocity vs Instaneous Velocity

    I just need some clarification. In a lab that i did, a metal ball goes down a slanted ramp, onto a horizontal ramp of d distance, and then goes airborne (off the table). The instant the ball enters the horizontal ramp a timer is started, and - when it goes airborne - the timer is stopped. Thus...
  14. J

    Trace - Integration - Average - Tensor Calculus

    Hi Let D be an anisotropic tensor. This means especially, that D is traceless. \mathrm{tr}(D) = 0 Apply the representating matrix of D to a basis vector S , get a new vector and multiply this by dot product to your basis vector. Than you got a scalar function. Now integrate this...
  15. L

    Average Velocity vs Average Velocity discrepencies?

    This question is about a discrepency between the method of finding average velocity via "change in distance over change in time" and the other method of "instantaneous velocity + instantaneous velocity all divided by 2" If I find average velocity of various points on a position vs position...
  16. T

    MHB Find Average Time for Completion of Two Tasks with Joint MGF

    If the joint moment generating function of X and Y is M X,Y (t1, t2) = 6 / (1-t1) * [(1/(2-t2)) -1/(3-(t1+t2))] and X,Y are the times AT WHICH the two successive tasks are completed, find the average time for completion of the two tasks. Also find the moment generating function of the time...
  17. S

    Determine speed of bar and average frictional force

    Homework Statement Large metal bars can be driven into the ground using a heavy falling object. What I have here is a 2000 kg falling object and a metal bar of 400 kg. The falling object strikes the bar at a speed of 6.0 m/s. It comes to rest on the bar without bouncing. As a result of the...
  18. L

    Three approaches to magnitude of average velocity

    Is there such a thing as magnitude of average velocity? If so, is it one of these? Suppose I have to position vectors. \stackrel{\rightarrow}{r}= 1_x + 2.2_y and \stackrel{\rightarrow}{r}_2 = 2_x + 0_y And the distance between the vectors is Δ\stackrel{\rightarrow}{r}=...
  19. B

    What is the Average Speed Computation Problem on a Hill?

    Homework Statement The problem is in the provided link (it is questions 2.2) http://www.docstoc.com/docs/3817109/Chapter-Problems-A-car-travels-up-a-hill-at-a Homework Equations The Attempt at a Solution I understand the duration of time it takes to go up the hill is a larger time...
  20. N

    Average Rate of Change for f(x) = 5x^2 - 8x from x = -1 to 4

    Homework Statement Consider the graph of the function f(x) = 5x^2 - 8x Determine the average rate of change as x changes from -1 to 4 The Attempt at a Solution f(4) - f(-1) / 4 - 1 The answer is not correct according to the answer sheet. :(
  21. D

    Finding the average concentrations given average Keq

    Homework Statement How would I find the average concentrations of Fe(SCN)+2, Fe3+, and SCN- where the equation is Fe3++ SCN-→Fe(SCN)+2 and the Keq was found to be 394. Homework Equations I know the equation for Keq=[Fe(SCN)+2]/([Fe3+]*[SCN-]) but I have no idea how what other equations...
  22. L

    Darts Statistical Lab with average, SDM, and probability

    Homework Statement Darts Lab: In lab, my group threw 100 darts and the class had a total of 1000 darts thrown. The target was between bins 24 and 25 I calculated all of the following: Table IIa: (mean of means) = 24.80 (standard deviation of the means) = 0.48 
(a) Compare (the...
  23. S

    What to plot as the errors for a moving average plot of temperature?

    I have been monitoring the temperature of a mirror surface placed outside at night. The temperature is measured at 10s intervals and so, as you can imagine, a plot of the data for one period is quite noisy. I have therefore decided to "smooth" the data by plotting a moving average over a...
  24. R

    How fast, on average, does the gas come out of a rocket's nozzle?

    For example, in the SSET (Space Shuttle External Tank), how fast does the burnt fuel (liquid hydrogen and oxygen) exit the nozzle at its bottom?
  25. Square1

    Are there better methods for finding the average value of a function?

    Hey so I am in a second semester calculus class and we are learning about the average value of the function. We are presented the following formula: (1/(b-a)) ∫a to b f(x) dx for a ≤ x ≤ b This is basically doing (x1+...xn)/n, except for infinitely many numbers over the interval...
  26. T

    How to derive an average output from a triaxial accelerometer

    Hi I am measuring the acceleration of an oscillating body with a triaxial accelerometer. I want to derive some kind of vector average of the 3 channel output. Someone suggested using x= √(a squared + b squared + c squared) ... where x is the vector average and a, b and c are the...
  27. D

    Help with average velocity during a time interval

    Homework Statement The position of a particle in meters moving along the x-axis is given by: x=21+22t-6t^2 Calculate the average velocity of the object in m/s during the time interval t=1s to t=3s. Homework Equations x=21+22t-6t^2 t=3 ; t=1 v avg. = Xf - Xi/Tf - Ti = Δx/Δt don't...
  28. D

    Can Calculus Prove Average Solar Irradiance is a Quarter of Total?

    Homework Statement I am trying to show that the average solar irradiance over Earth's surface is 1/4 of the total solar irradiance using only calculus. Homework Equations Solar Irradiance = S_{o} Irradiance = F = S_{o}cos(θ) The Attempt at a Solution Using geometry, I can easily...
  29. M

    How Do You Calculate Average Velocity in Projectile Motion?

    Homework Statement A ball is projected upward at time = 0.0 s, from a point on a roof 10 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 98.8 m/s Consider all quantities as positive in the upward direction. The average velocity of...
  30. E

    Finding the pdf of the average of n independent random variables

    Homework Statement The n random variables X_{1}, X_{2},..., X_{n} are mutually independent and distributed with the probability density f(x)=\frac{1}{\pi(1+x^{2})} i) Find the probability density of the average Y=\frac{1}{n}\Sigma^{i=1}_{n}X_{i} ii) Explain why it does not converge...
  31. I

    Interested in average household energy consumption in 2011

    Particularly, what do the figures look like for the amount of energy consumed per household in 2011? As a comparison, how much energy have you consumed in 2011? Also, I'm interested to know what kind of fuels or carriers are most often used. I'm tempted to believe that coal is probably one...
  32. S

    Speed related to Average Velocity

    Homework Statement I am having difficulty thinking about this problem. How is speed related to average velocity? A car travels along a straight line at a constant speed of 47.0 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average...
  33. DataGG

    Calculating Average Lifetime of Particles at Rest

    Homework Statement A beam of unknown particles travels at a speed of 2.5 x 10^8 m/s. When the particles are moving at this speed, their average lifetime is found to be 7,3 x 10^-8 s. What is their average lifetime when at rest? Homework Equations Well, Lorentz transformation for time...
  34. R

    Why can't i apply the simple average velocity formula?

    I'm doing a homework problem (i already know the answer) and i came across an error in my logic/application of the formula Vavg = (v + v0)/2. Hopefully you can help me understand why it's incorrect to use the formula. x = 12t2-2t3 describes a particle position. the derivative of x = 24t-6t2...
  35. J

    Total energy of a star in terms of average temp.

    Homework Statement The problem I am doing is problem 1.55 in Schroeders Intro to Thermal Physics. Unfortunately, I have to come here for help a lot because the office hourse are not until after the homework is due...In any case, the first part of the question was to show that the potential...
  36. C

    How do I find the average velocity of an electron?

    Homework Statement A current of 1600A exists in a rectangular (0.4-by-16cm) bus bar. the current is due to free electrons flowing the wire at an average velocity of v meters/second. If the concentration of free electrons is 10^29 electrons per cubic meter and if they are uniformly dispersed...
  37. D

    Average torque of a rotational freefall

    Hi all, this is not actually homework or similar but the board seemed as the appropriate place for the question. I have an arm of 1m length pointing upwards from a rotation axis, on the end of the arm is a mass of 1kg, upon release the arm starts rotating downwards due to gravity (no other...
  38. B

    Simple average question using sig figs within ± 0.0 of uncertainty?

    Simple average question using sig figs within ± 0.0 ? Homework Statement Consider the following measurements of mileages: 23.8 mph, 20.1 mph, 26.5 mph, 20.7 mph, 21.7 mph, 27.6 mph, 30 mph, 28 mph, 27.4 mph, 34.3 mph, 26.5 mph, 32.7 mph. What is the average mileage (using...
  39. R

    How much current/voltage on average is produced by means of induction?

    By spinning a magnetic field in the presence of conducting wire, how much voltage/current is produced? Thanks.
  40. D

    Waveforms, rms, average, offsets

    Hi guys I'm trying to work out average and rms values of two different waveforms. One is a sinusoidal wave, the other a ramped trapezoid (I think that's right). The sinusoidal wave has a peak to peak voltage of 11v and the offset is alleged to be 9-15 = -6v. This is something I've been told...
  41. D

    Finding Average Shear Strain in a flexible connection of rubber and steel

    Homework Statement [See Attachment] Given: Thickness, load, G Find:γ and horizontal displacement. Homework Equations τ=γG Angle change should be the shear strain. The Attempt at a Solution I tried plugging 800 into tau and the given value of G to get γ, but that isn't...
  42. C

    Finding the average using integration

    Homework Statement Find c such that fave = f(c) c1 (smaller value) = ? c1 (smaller value) = ? f(x) = 6x/(1 + x2)2 Average value (i.e. the integral) was found to be 12/5 Homework Equations 12/5 = 6x/(1 + x2)2 The Attempt at a Solution 12/5 = 6x/(1 + x2)2 12/5 =...
  43. A

    Average value in superposition question

    Hi there. A quick question: When calculating the average energy (or any value) of a particle which is in superposition, why the sums have different summation index (n,m)? Thanks!
  44. L

    What is the Average Monthly Weight Gain for a Baby Over a Specific Time Period?

    Homework Statement The weight of a baby measured over an 11-month period is given in the weight chart below for this problem. Weight (lb) Age (months) 6.6 0 (birth) 7.4 1.0 9.6 2.0 11.2 3.0 12.0 4.0 13.6 5.0...
  45. N

    Average Velocity in One Dimension

    A question about the average velocity of bodies undergoing one-dimensional motion and a constant acceleration (gravity in this case). A case scenario. Suppose that initially, I throw a stone into the air at a height h. For the sake of argument, let's suppose that even though I threw the...
  46. C

    How Do You Calculate Average Speed from Displacement-Time Data?

    Homework Statement Use the data table of displacement time data to get a line of best fit using your Ti-83 calculator. Once you have the equation, graph it so that you can answer the questions 1-5 that follow. Assume that the data below is for an object that is launched vertically upwards...
  47. G

    Triple Integral and finding the average

    Solve the Integral in cylindrical coordinates ∫∫∫ dxdydz/(sqrt( x^2 + y^2 + (h-z)^2) B Where B is the Ball with a Radius R around (0,0,0), and the parameter h is greater than R. And then infer the average on that ball B with radius R of the distance opposite to the point (0,0,h). I...
  48. J

    Finding average speed on a velocity vs time graph

    Hello, Again I find my self struggling on a question I had on a test, as my teacher is a "general studies" teacher, she is not much help with physics. the question is: What is the average speed of the car for the 10 second interval? I have uploaded the graph provided, if you can't...
  49. O

    Slope: Average vs. Instantaneous Change

    Hello! What is slope. Is it rate of "average change" or "rate of instantaneous" change? Please elaborate
  50. S

    Average Torque on an Induced Current Loop

    Homework Statement A rectanglar loop of wire encloses an area A, has a resistance R and a self-inductance L. The loop is suspended from the mid point of one of its sides and placed in a horizontal oscillating magnetic field B = B0 sin ωt such that the field makes an angle θ with the normal to...
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