What is Average value: Definition and 107 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

    Average value of f(x,y) = xy in quarter circle x^2 + y^2 < 1 in Q1.

    Here is the problem: Find the average value of f\left(x, y\right) = x\;y for the quarter circle x^2 + y^2 \le 1 in the first quadrant. Here is what I have: Average value equation is \frac{1}{Area\;of\;R} \iint_{R} f\left(x, y\right) dA f\left(x, y\right) = x\;y =...
  2. C

    NBA Salary Growth: Solving for Average Salary and Future Projections

    If the average salary S of an NBA player is increasing and can be modeled by: \frac{dS}{dt} = \frac{1137.7}{\sqrt{t}} + 521.3 and t = 5 is 1985. a. Find the salary function in terms of the year if the average salary in 1985 was $325,000. b. If the average salary continues to increase at...
  3. C

    Quick help on average value problem please

    I am in a time crunch and I am stumped... I need to find the average value function of f(x) = (3x+5)^2 on [1, 2] help please..
  4. C

    Quick help with average value function problem please

    I am in a time crunch and I am stumped... I need to find the average value function of f(x) = (3x+5)^2 on [1, 2] help please..
  5. C

    What is the average value of this function on the interval [0,1]?

    Find the average value of \int_{x}^{1} cos(t^2)dt on [0,1] I have no idea where to even begin..
  6. tandoorichicken

    Calculating Average Value of y=x^2√x3+1 from 0 to 2

    Hmmm... got this one wrong What is the average value of y = x^{2}\sqrt{x^3+1} on the interval [0,2] ? Okay, so another average value problem right? f(b) - f(a) = f'(c)(b-a) f(2) - f(0) = 2f'(c) 12 = 2f'(c) So then the average value is 6 right?
  7. tandoorichicken

    Troubleshooting the Average Value of a Function

    I forgot the formula for the average value of a function. Is that f(b) - f(a) = f'(c)(b-a) or am I thinking of something else?
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