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. M

    Need to find the net force and the average force .

    Need to find the net force and the average force... 1. Homework Statement A bullet of mass 12 g strikes a stationary fixed block of wood at a speed of 400m/s, penetrating to a depth of 3.0cm. Calculate the average net force acting on the bullet while it is in the wood. Calculate the average...
  2. N

    Period of arbitrary amplitude pendulum using average speed

    Homework Statement A simple pendulum of length L is pulled aside to angle θm then released from rest. For arbitrary angle θ on the path of motion the acceleration along the path is -gSinθ. The speed at this point is V(θ)= √[2gL (cos θ - cos θm)]. Find the period T of the pendulum (do not...
  3. L

    Finding number density and average distance between molecules

    Homework Statement At 0.0° C and 1.00 atm, 0.95 mol of a gas occupies a volume of 0.0213 m3. (b) Estimate the average distance between the gas molecules.
  4. T

    Average Value and Area in Polar

    Homework Statement Let Q be the region bounded by r=sin(3θ) in the first quadrant. Find the area of Q. Find the average distance of points in Q from the origin. The Attempt at a Solution I thought I could calculate area like so: \int_0 ^{pi/3} \int_0 ^{sin(3θ)} sin(3θ) dr dθ This gives...
  5. K

    Average Angular Acceleration of a CD

    Homework Statement A CD has a playing time of 59.8 minutes. When the music starts, the CD is rotating at an angular speed of 460 revolutions per minute (rpm). At the end of the music, the CD is rotating at 202 rpm. Find the magnitude of the average angular acceleration of the CD. Express...
  6. P

    Solving the average shear and normal forces

    Homework Statement View image below Homework Equations The Attempt at a Solution I don't understand where the normal and shear forces are applied. Are there one of each on both inclined planes or is there just one normal force and one shear force? If you could provide a drawing I...
  7. P

    Find the average shear stress at each pin

    Homework Statement View image for all details Homework Equations tao = V/A The Attempt at a Solution I went ahead and solved the force at BC and the x and y components at A, but I feel as though my solutions are incorrect. At BC I have F = 825 kN (up and to the left), A_x = 714.5...
  8. M

    Calculate Average Net Force of 20g Bullet Striking Wood

    A bullet of mass 20 g strickes a fixed block of wood at a speed of 320m/s. The embeds itself into the block of wood, penetrating to a depth of 6.0cm. Calculate the average net force acting on the bullet while it is being brought to rest.
  9. R

    Physics problem to fine average force

    A set of crash tests consists of running a test car moving at a speed of 11 m/s (24.2 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 57 kg (125.4 lbs) dummy is found to move a distance of 0.81 m from the moment the car touches the wall to the time the car is...
  10. B

    Average velocity vs Final velocity

    Homework Statement Shouldn't average velocity multiplied by 2 be equal to final velocity. We were doing a lab and we calculated an average time of .54 seconds to travel 1.92 meters. Multiplying the average velocity by 2 gives an extremely different answer than vf=gt. I know there is...
  11. DaveC426913

    Why Use Weighted Averages in Survey Results?

    We got some results back from a company survey today. The speaker showed us the numbers and told us they had weighted the averages. Say, there were two questions: All the time | often | sometimes | rarely How well does our company communicate? 60% |...
  12. O

    Average acceleration problem

    Homework Statement The average speed of a nitrogen molecule in air is about 6.70 multiplied by 102 m/s, and its mass is about 4.68 multiplied by 10-26 kg. (a) If it takes 1.80 multiplied by 10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in an...
  13. R

    Calculating average horsepower of an elevator help

    Hello. I hope someone here can give me some advice for solving this problem for an introductory mechanical engineering course. Below is the problem statement verbatim, and them my attempt at solving it. Advice and guidance is greatly appreciated! Homework Statement Here is the problem...
  14. J

    Calculating the Weighted Average of Two Graphs

    i have an excel file containing 2 graphs [R & V], and their x & y coordinates in 4 separate lists [the X coordinates of R, the X coordinates of V, the Y coordinates of R, the Y coordinates of V] i need to calculate the X & Y coordinates of a 3rd graph through a weighted formula that takes 55%...
  15. T

    Average value of a function over involving triple integral

    Homework Statement We define average value of function over a solid to be f = 1/Volume int int int f(x,y,z) dV So find the average value of the function f(x,y,z) = x^2z+y^2z over the region enclosed by paraboloid z = 1-x^2-y^2 and the plane z = 0 The Attempt at a Solution Actually...
  16. D

    Calculate Average Power Output of Man Climbing 1576 Steps

    A man runs up 1576 steps in 9minutes 33sec. If the height gain of each step was 0.20m, and the mass of the runner was 70.0kgs, what was average power output during climb? I used P=W/T & W=FD W=70kg(1576)0.20=22,064J P= 22,064J/573s = 38.5 W answer given is380W What am I missing?
  17. M

    Average of a quantity in all directions

    Homework Statement I have to compute the average of A in all directions for a sphere of radius R. For the direction r, A is defined as: A=\int_0^R n(r)dr where n(r) is the density profile of the sphere. The answer should be \langle A\rangle=\frac{4}{3}\left\langle n \right\rangle R 2. The...
  18. M

    Average Angular Acceleration of a Music CD over 75 minutes

    A CD has a playing time of 74.2 minutes. When the music starts, the CD is rotating at an angular speed of 488 revolutions per minute (rpm). At the end of the music, the CD is rotating at 215 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s^2...
  19. P

    Computing Thermal Average for a Free Real Scalar Field

    Homework Statement Homework EquationsHi! I read a book where a free real scalar field with Hamiltonian H = \int \dfrac{\mathrm{d}^{3}p}{(2 \pi)^{3}} \, E_{\vec{p}} a_{\vec{p}}^{\dagger} a_{\vec{p}} is beeing discussed. Note that: E_{\vec{p}} = \sqrt{\vert \vec{p} \vert^{2} + m^{2}}...
  20. D

    Calculating the Average of 2 Functions

    Homework Statement My question pertains to taking the average over a particular period that is composed of 2 functions. For example, from [0, 5ms] the function is defined by 1-e^(-t/1ms)and then by e^(-t/1ms) from [5ms, 10ms]. Will the average from 0-->10 simply be the following...
  21. B

    Prove that if m is the average of x1,x2, ,xk, then

    Homework Statement http://img440.imageshack.us/img440/9242/captureyeq.jpg Uploaded with ImageShack.us Homework Equations Given in problem statement. The Attempt at a Solution Basically I've come up with the contrapositive, but I'm unsure of how to proceed with the proof. Can...
  22. V

    What is the average price per share for John's holdings after Date 4?

    Dear all, Although the following question involves some terms using finance, I post it here since it seems to involve some probability. I hope that it will be fine. Thank you very much for your help. --------------------- Problem: Suppose that John buys shares in only one company...
  23. J

    What is the average of (Ri-1/N*Sum[Ri])^2 The sum is from i=1 to i=N.

    What is the average of (Ri-1/N*Sum[Ri])^2 The sum is from i=1 to i=N.
  24. E

    Chemistry Average number of air molecules.

    Homework Statement Hey guys. Hope you can help me out on this one. so here's the question: At an altitude of 50km the average atmospheric temperature is 0^oC. What is the average number of air molecules per cubic centimeter at this altitude. Homework Equations M = 28.97 g mol^-1...
  25. 8

    Average value of function, answer check

    Homework Statement Find the average value of the function u(x)= 10xsin(x2) on the interval [0, ∏1/2] (Sorry, I can't figure out how to make the square root symbol)Homework Equations The Attempt at a Solution For the integral of u(x), I got -5cos(x2) I substituted 0 and ∏1/2 and got 10. then...
  26. C

    Average velocity is measured through distance

    Is average velocity equal to the average of two instantaneous velocities. I had a question on a calculus exam that gave an equation to a particle moving and was told to find both the average velocity on the time interval [0,1] and the instantaneous velocity at 1. I took the derivative of the...
  27. M

    Experiment to Measure Average Force when Hitting Hockey ball?

    Homework Statement Two girls are arguing about which is able to hit a hockey ball harder. Describe an experiment which they could carry out to measure the average force between the stick and ball during time of contact. Homework Equations Force * Time=Change in Momemtum (Mv-Mu) The...
  28. T

    Average force and a balance []

    I have to deliver this problem resolved in 4 hours, I didn't think it was going to be so hard... Homework Statement A man of mass M is on the top of a balance with a very high damping coefficient. In a given instant he throws a ball of mass m vertically, catching it again later. a)...
  29. C

    Average value of sin(i) in radial velocities (exoplanets)

    When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to m\sin i\text{ where }i is the orbital inclination of the planet with respect to our line of sight and m is the planet mass. I've heard that even though the inclinations are...
  30. E

    Average Power of a Car: How to Calculate and Understand It

    Homework Statement mass of a car is 2000 kg that can go from 0-120 km/h in 3.5 seconds. What is the average power? Homework Equations I know that the average power is Work/time, or (force * displacement)/time = F*average velocity. My only question is how to find the force of the car...
  31. U

    Average engineering School and High GPA or Top Engineering School and lower GPA

    So I am currently in an average ABET EE program and have a 4.0, but I am thinking of transferring to the top 30 engineering school about an hour away. I was wondering which matters more, GPA or institution? Both have a great college fair, and both are ABET accredited. And, I am not saying I...
  32. S

    Magnitude of average acceleration?

    I haven't done anything Physics related in 2 years (high school) and am trying to get back into being familiar with Physics, Science, and mathematical terms for an upcoming class. Homework Statement A gazelle starts from rest and runs in a straight line 29° north of west. After 36s of...
  33. S

    Calculating Instantaneous Velocity in Calculus

    Homework Statement A ball is thrown into the air a velocity of 49 ft/s. Its height in feet after t seconds is given by y=49t-10t^2. A. Find the average velocity for the time period beginning when t=3 and lasting 0.01 s: 0.005 s: B. Estimate the instantaneous velocity when t=3.Homework...
  34. S

    Find the average value in a calculus approach

    Homework Statement Find the average value of : f(x) = 4sinx + 4cosx on the interval [0, 16pi/6] Average value: ? Homework Equations Integrals The Attempt at a Solution 1/ [(16pi/6) -0] ∫ from 0 to 16pi/6 4sinx + 4cosx dx [3/8pi] ∫ from 0 to 16pi/6 4sinx + 4cosx dx <------simplify...
  35. L

    Average Rate of Change/Differentiation Problem

    If the average rate of change of a function f over the interval from x = 2 to x= 2 + h is given by 7e^h -4cos(2h), then f ' (2) = ? This is what I got: [f(2 + h) - f(h)]/h = 7e^h -4cos(2h) I know we are supposed to used Mean-Value Theorem, I just don't get how to do it.
  36. I

    Which direction is the average acceleration going?

    Homework Statement An object moves along a circular path with a constant speed, |v|. The average acceleration in going from A to B is 1. south 2. zero 3. west 4. north 5. east 6. none of the others Homework Equations a = Δv / Δt tangential acceleration = mv^2 / r...
  37. N

    Average Acceleration Units Problem

    1. An electric train initially moving at 25km/h accelerates to 35km/h in 20s. Find its average acceleration in m/s^2. G: v1 = 25km/h v2 = 35km/h Delta t = 20s R: Aav 2. Aav=(v2-v1)/delta t 3. = (35km/h-25km/h)-20s The problem is that the velocities are in km per...
  38. S

    Earth Science: Average Rate of Sediment Deposition

    Homework Statement Link of picture that the information below is referring to: http://i56.tinypic.com/283lv.jpg You encounter the sedimentary rock outcrop shown above while you are out hiking. You collect rock samples from points A-D and go back and measure their ages in your isotope lab...
  39. G

    Solving for Car's Acceleration, Time, and Average Speed

    Homework Statement A car is initial at rest. It accelerates over a distance of 1250m and reaches a speed of 112 km/h. Find: A) the acceleration for the car B) the time it took for it to reach this final speed C) the average speed Homework Equations A = delta V/ delta T or v^2 = V...
  40. J

    How to solve for average velocity on a distance time graph?

    Homework Statement Hi i need some help with this question: A teacher drives to work at a average velocity of 80km/h. He forgets the test and INSTANTLY turns around and travels back home at 120km/h. What is the average speed for the trip? Do i have to find instantaneous velocity? I am not...
  41. O

    Average Velocity and Average Speed of Integral

    Homework Statement An object moves with velocity v(t) = −t2 +1 feet per second between t = 0 and t = 2. Find the average velocity and the average speed of the object between t = 0 and t = 2 Homework Equations \frac{1}{b-a} \int_a^b f'(x) dx avg value of a function The Attempt...
  42. T

    What average force is exerted on the ball during the contact time?

    Homework Statement A 0.25 kg ball, initially at rest, is hit with a bat in the x-direction while held 1.00 meter above the ground. If the ball hits the ground 20 meters away and was in contact with the bat for 0.10 sec, What average force was exerted on the ball during the contact time...
  43. P

    What Was the Average Velocity of the Hiker During the Trip?

    Homework Statement a hiker walks 6.7 miles to the east in 5.1 hours. then turns around and walks 1.1 miles to the west in 1 hour. what was her average velocity during the trip? A 1.2mph B 1.3mph C .92mph D 3.9mph Homework Equations not sure how to write what i used The Attempt...
  44. G

    Direction and magnitude of the average acceleration

    [b]1. A ball is dropeed from a height of 2.5m and rebounds to a height of 2.1m. If the ball is in contact with the floor for .70ms determine 1: direction and 2: the magnitude of the balls average acceleration due to the floor I know the equation for average acceleration = change in...
  45. W

    Can anyone help with an average speed problem?

    Homework Statement A racing team of 3 drivers drove a 24 hour event in shifts. The first driver drove only one fourth of the race but averaged 140km/hr. The second driver drove one third of the race at an average speed of 170 km/hr. The last driver drove the remainder of the race at 160...
  46. R

    Difference between Average Speed & Average Velocity in Velocity-Time graphs?

    I just want to know what is the difference on how to find Average velocity and Average speed when I try to find it in Velocity-Time graphs Also how do you find distance traveled and displacement in these velocity-time graphs. Thanks in advance for your help. Please use fairly simple...
  47. C

    Arrow hitting a target average force question

    Homework Statement A 8.0×10−2 kg arrow hits the target at 25 m/s and penetrates 3.8 cm before stopping. Homework Equations What average force did the target exert on the arrow? What average force did the arrow exert on the target? The Attempt at a Solution I found the...
  48. C

    What is the average magnetic dipole moment?

    Though this might be absurd, I would seriously like to know the average magnetic dipole of a magnet. For example, you might consider a regular magnet in a remote control car's motors, or any other suggestions too. And I have one more doubt- I know that e.m.f=-d(phi)/dt and phi=integral(B.dS)...
  49. C

    Flat Plate Heat Exchanger. Find average convection HT coefficient

    Homework Statement In this flat plate heat exchanger, rippled plates (0.3 m thick each) create channels that allow heat transfer between a hot and a cold fluid. Conduction occurs then from the heat temperature difference between the two fluids while convection occurs as the fluids move...
  50. L

    Calculating Average Speed: Step-by-Step Guide for East and North Travel

    Homework Statement A car travels east at 86 km/h for 6 h. It then travels 50.0° east of north at 112 km/h for 6 h. (a) What is the average speed for the trip? How do I solve for the average speed?
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