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

    MHB Calculating Number of Sides in an n-gon with an Average Angle of 175°

    The interior angles of an n-gon have an average measure of 175 degrees. Calculate n.
  2. S

    Which body has the higher average speed?

    Homework Statement Two bodies travel the same distance. One body travels half of the distance with the speed V and the other half with the speed 2V. The second body travels half of the time with the speed V and the other half of the time with the speed 2V. Which of the bodies has the higher...
  3. Graeme M

    Deriving average surface temperature of a blackbody sphere?

    I have been reading about climate change recently and I have run into a problem understanding the Earth's energy budget. I will try to summarise my question but am happy to try to expand if needed. Bear in mind I am just an interested average Joe with little science background and probably a...
  4. Z

    Problem: Determine the maximum value of the average normal stress

    Hi guys. Please look at the uploaded picture. Normal stress is difined as: σ= P/A. And the Maximum normal stress σ = P/ (b*h/cos(θ)) ?? The right answers should be σAB= 97,7 MPa and σBC = -66,5 MPa. But how do I calculate it? What I have tried: Force AB: 40* sin(60deg) = 34,641 kN...
  5. C

    Average magnitude of force during a 0.4 second impact

    Homework Statement A 40kg branch falls 5.5m and lands on a roof. The roof withstood the the impact. Homework Equations If the impact time was 0.4 second calculate the magnitude of the average force exerted on the roof during the impact. The Attempt at a Solution F=ma doesn't seem right...
  6. E

    Sequences of periodic functions converging to their average value

    Homework Statement Let f be a 2π-periodic function (can be any periodic really, not only 2π), and let g be a smooth function. Then lim_{n\rightarrow∞}\int^{B}_{A} f(nx)g(x) converges to \frac{1}{2π}\int^{2π}_{0}f(x) The Attempt at a Solution So far, I've come up with somewhat of...
  7. M

    Finding average acceleration with two sets of velocity vecotors

    Homework Statement A jet plane is flying at a constant altitude. At time t1=0 it has components of velocity vx=95m/s, vy=115m/s. At time t2=33s the components are vx=172m/s, vy=35m/s. Find average acceleration. Homework Equations avg acceleration=vfinal-vinitial/change in time The...
  8. M

    How to expand the average <(N - <N>)^2>

    Basically I would like to know how to expand: \left\langle(N - \left\langle N \right\rangle)2\right\rangle <(N - <N>)^2> Where < and > represent \left\rangle\right\langle and denote the average of the quantity the enclose. So this is pretty much the average of [N - N(average)] 2...
  9. RabbitWho

    Medical Above average effect in psychology

    http://en.wikipedia.org/wiki/Illusory_superiority My book has a survey in it that is supposed to show you if you have these biases or not, but it seems so silly to me. I can see how it applies to intelligence, assuming that we are right all the time is a pretty adaptive bias in a lot of...
  10. M

    Calculating Average Angular Velocity

    Homework Statement At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by theta(t)=246t-20.6t^2-1.47t^3 Calculate the average angular velocity for the time period from t=0 to the time calculated when the angular velocity of...
  11. mesa

    Checking Average Atoms in 1 m^3 of Atmosphere at STP

    So I need a check on my calculations for the average number of atoms in a 1 meter cube of atmosphere at STP. I came up with 88.14 mols, here is how I did it: First I calculated the average amu using percentage in air by Nitorgen 78.08% @ 14.007 amu Oxygen 20.95% @ 15.999 amu Argon...
  12. O

    Weighted average of arbitrary k points from a line

    Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a weighted barycenter x_o=(o_i*x_i)/(o_1+o_2+...+o_k) also belongs to that line (assume o_i are arbitrary weights)? Does the choice of weights restrict the solutions (ie, a...
  13. X

    Average velocity of vehicle

    Homework Statement A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and the distance travelled. Homework Equations Average velocity = Total distance/ time taken The Attempt at a Solution Acceleration = (26-2)/12...
  14. J

    Average force applied by bullet

    Homework Statement What is the average force applied by a 75 g bullet that leaves a gun at 1350 m/s and hits a target 75m from the barrel of the gun? Homework Equations F = ma The Attempt at a Solution First I had the equation F = ma, and began filling in all the variables I could...
  15. H

    Calculate the average amount of power that the heart delivers

    Homework Statement When a human heart during a heartbeat pulls together the overpressure in the outwardgoing arteries is about 16 kPa. Every minute the heart drives 5 liters of blood around in the bloodstream. Calculate the average amount of power that the heart delivers Homework...
  16. X

    Need Help with an Average Acceleration Problem

    A car traveling with a constant speed of 14 m/s due west comes to an intersection where it makes a turn onto a southwest (45 degree) street. The car takes 5.2 seconds to complete the turn and the speed of the car does not change during this time. Find the average acceleration of the car. Report...
  17. W

    How Do You Calculate Average Velocity for Different Directions?

    girl walks 5.0 km [w] then 2.0 km [e] in 1.2h. determine averagee velocity. Please show work
  18. S

    Find the average power over one cycle

    Homework Statement The problem and its solution are attached as TheProblemAndSolution.png. Homework Equations Integration P = VI V = RI The Attempt at a Solution I think Wolfram Alpha “says” ( http://www.wolframalpha.com/input/?i=integrate+900sin%5E2%28377t%29+dt+from+0+to+pi ) that...
  19. R

    On average how many rolls will it take to roll a 6?

    We have a simple, fair, 6 sided dice, and we ask the question - how many times will i have to roll it (on average) to get a 6? I made an experiment (although with only 50 rolls) and i got, that the average was around 5.4.
  20. Z

    Difference Quotient - average rate of change

    Homework Statement Original function f(x) = -x^2+5x-2 I have calculated the difference quotient as -2x-h+5 Then use difference quotient to calculate the average rate of change: for the following x=2 and x=2+h I need this to go on to the next part of the question and i wanted to ensure...
  21. S

    Free Fall Lab Question: Calculating Average Acceleration and Velocity

    Homework Statement Within this lab I was supposed to perform a virtual experiment and find the rate a ball dropped on the moon, mars, and earth. I have recorded all of my results in the table below. My problem is that my average velocity on Earth ended up as 8.9 m/s, and I thought that the...
  22. O

    Average speed of a moving ball

    Hey guys so I'm stuck and only have a couple tries left meaning I've lost quite some marks on this question already and I can't risk anymore so the question is... A ball moves in a straight line (the x-axis). The graph in the figure (Figure 1) shows this ball's velocity as a function of time...
  23. D

    Schools What do you think is needed to get full tuition at your average university?

    I was thinking it was something among the lines of 1300/1600 SAT or 29 ACT and Top 10% of your class or 3.5 GPA, but I'm not sure and am looking for confirmation. Thank you.
  24. jegues

    Calculating the Average Power of a Signal

    Homework Statement Find the average power of the signal, x_{1}(t) = 5cos(2\pi t + \frac{\pi}{10}) - 6sin(10t + \frac{\pi}{8}) Homework Equations The Attempt at a Solution P_{avg} = \frac{1}{T_{1}} \int_{0}^{T_{1}} 25dt + \frac{1}{T_{2}}\int_{0}^{T_{2}}36dt P_{avg} = 61...
  25. T

    Average force exerted by ball on the wall

    Homework Statement A superball is to bounce elastically back and forth between two rigid walls at a distance d from each other. neglecting gravity and assuming the velocity of superball to be horizontal .Find the average force being exerted by the superball on each wall is ?Homework Equations...
  26. L

    Average values for pulse width modulation

    I am looking for average values of the signal-to-noise ratio for pulse width modulation and for a direct signal?
  27. A

    Calculating average atomic mass

    The relative abundance of various isotopes of silicon is as Si(28) = 92.25%, Si(29) = 4.65% and Si(30) = 3.10 % . Calculate the average atomic mass of Silicon. Ans : 28.11 u Attempt. : I don't know how to start this problem .
  28. H

    Calculating Average Force for a 1,662 kg Car in 19 secs

    A 1,662 kg car goes from 14 m/s to 29 m/s in 19 secs. What is the average force acting upon it? Write your answer to two decimal places. Attempt: Mass = m = 1,662 kg Initial Velocity = Vi = 14 m/s Final Velocity = Vf = 29 m/s Time = t = 19 secs Acceleration = a = Δvelocity/time =...
  29. T

    Finding the max value of the average normal stress

    Homework Statement Here is the question with the solution: The Attempt at a Solution I understand the first part where they find the forces by summation of moments. However I don't understand how they got that area. Why would they take the diameter (0.016) and subtract it from the length...
  30. J

    Average waveform or calculated values?

    I have an experiment where I calculate a value based on a waveform acquired by a digitizing oscilloscope. Since the signal is very noisy, I need to average the results many times to get a reasonably accurate value for each measured data point. My question is how should I spend the time averaging...
  31. A

    Find the average velocity in the time intervals

    Homework Statement The position versus time for a certain particle moving along the x-axis is shown in Figure 1. Find the average velocity in the time intervals 0 to 2 s, 2 s to 4 s, 0 to 8 s. Homework Equations The Attempt at a Solution I do not understand the question? I...
  32. G

    Derive 1-dimensional motion from average acceleration (no calculus)

    Starting with the expressions for average acceleration (Change in Velocity over Change in time), average velocity at constant acceleration; algebraically (NO CALCULUS) derive the equation for one-dimensional motion that relates displacement to the acceleration, assuming acceleration is constant.
  33. G

    Physics: 1d Motion-Instantaneous Velocity vs Average.

    Trying to create a table with time and instantaneous velocity. (the tables- http://i.imgur.com/8DZsu.png ) How do I go from using the Average Velocity to the Instantaneous Velocity? Instantaneous Velocity is the V_avg at t_1 + (delta-t)/2 how do I use this with my data.
  34. T

    Apparent forces problem, train of average speed and a difference in weight

    Homework Statement While taking an eastbound train to work, a passenger of fixed mass finds that she weighs 542N. On the way home she weighs herself again while the train is at full speed and finds she weighs 543N. If she works 50km from home, how long is her commute if she lives at 40°S...
  35. D

    How to Calculate Average Acceleration with a Non-Straight Graph

    Homework Statement Here's the graph: http://i.imgur.com/uUXPO.jpg What is the average acceleration between t=0s and t=2s? Homework Equations a avg = change in velocity / change in time ; (Vf-Vi)/(tf-ti) The Attempt at a Solution I know how to solve it if it was just a straight line where I...
  36. C

    What Is the Average Kinetic Energy of Ethane at 410K?

    Homework Statement Find the average kinetic energy in kJ/mol (including all degrees of freedom) of one mole of ethane at 410K. Homework Equations 1/2Mu^s = kT/2 u= avg. velocity E=n/2kT N=degrees of freedom The Attempt at a Solution C2H6 degrees of freedom - 3n-6 = 18...
  37. M

    Calculating Average Acceleration of a Bouncing Super Ball

    A 45.0-g Super Ball traveling at 30.0 m/s bounces off a brick wall and rebounds at 20.5 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.70 ms, what is the magnitude of the average acceleration of the ball during this time interval? Apparently the...
  38. M

    Physics homeowork Average Velocity

    Hello everyone i need help in my physics homework my class is tomorrow and i ve been trying to solve it since 2 days but i don't now how to A driver moves 1/3 of the way between two cities with speed of 60 km/hour he continuous with speed of 90 km/hour find the average velocity? the car...
  39. S

    Why isn't rotation included when calculating the average energy of a monatomic gas?

    Greetings, this is my first post, though I have been reading these forums for a while. I understand that the average energy of each degree of freedom in a thermodynamic system in equilibrium is kT/2. My textbook says that for a monatomic gas particle, the only degrees of freedom that count...
  40. C

    Average Acceleration (gravity question)

    Hello. I was doing some physics and I came across a problem involving gravity. The problem was finding out how long (in disregaurd to atmosphere) long (time) it would take for a body to reach earth. I'm familiar with distance's derivatives, which give me: t=\sqrt{\frac{2D}{g}} where t=time...
  41. N

    What is the average speed for the entire trip?

    Homework Statement A commuting student leaves home and drives to school at an average speed of 40.0 km/h. After 24.0 min he realizes that he has forgotten his homework and returns home to get it at the same average speed. It takes 9.0 min to find the report, after which the trip to school 40.0...
  42. D

    Average Percentages over 3 years

    I am just having trouble with percentages. Lets say a town has a population of 1,000,000 in 2006 1,200,000 in 2007 1,800,000 in 2008 The percentage increase from 2006-2007 is 20% 2007-2008 is 50% So, what I want to work out is the AVERAGE percentage per year. The increase...
  43. PhizKid

    How do I calculate the average of uncertainties?

    Homework Statement Trial 1: 1.05 ± 0.05 m. Trial 2: 2.0 m. Trial 3: 1.5 m. Trial 4: 1.05 ± 0.05 m. Homework Equations Not sure The Attempt at a Solution So to add them up, I just add the "base" measurements" and then tack on the ± and stick in the "uncertainties" like so: 1.05...
  44. P

    Uncertainty of Average Acceleration

    Homework Statement You have determined the acceleration a_{i} of an object in free fall for i = 1 to n different time intervals. What is the algebraic expression for the uncertainty σ_{a,avg} in a_{avg}? (Use any variable or symbol stated above as necessary.) The answer box is formatted as...
  45. 1

    What is the Average Velocity of a Race Car on a Circular Track?

    Hi guys, sorry because I am quite confused. If a person runs a quartermile circular race track for 8 laps for 25.0 min, what is the average speed? What is the average velocity? Does that mean that the average velocity is zero m/s? Because the runner ends on the point where he started...
  46. R

    Average acceleration problem having trouble

    At a certain time a particle had a speed of 11 m/s in the positive x direction, and 1.3 s later its speed was 78 m/s in the opposite direction. What was the average acceleration of the particle during this 1.3 s interval? Homework Equations I have Vi=11m/s, Vf=78m/s and t=1.3 m/s The...
  47. V

    What is the Average Velocity of a Stone Tossed in the Air?

    Here is my problem: A stone is tossed in the air from ground level with an initial velocity of 20m/s. Its height at time t is h(t) = 20t-4.9t^2 m. Compute the stones avg velocity over the time interval [1.5,2.5]. I understand how to compute average velocity its Vavg=change in...
  48. V

    Average velocity of a falling object problem

    Homework Statement A falling object moves so that its height x above the ground at time t is given by the following equation: x = 100 m - (4.9 s-2)t2. Find its average velocity from t = 0 t t = 2 s. Homework Equations Average velocity = Δx/Δt The Attempt at a Solution I was...
  49. H

    Calculating Average Velocity of a Moving Train: Solving Kinematics Problem

    Hello, I have problem with this example. I don't speak English very well, so please forgive me if something isn't quite enough defined - as it should be in English Physics terminology. The train moves from the station with an acceleration a. After reaching velocity v moves farther with...
  50. 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...
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