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Topic: Mean value

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  Mean value theorem - Wikipedia, the free encyclopedia
In calculus, the mean value theorem states, roughly, that given a section of a smooth curve, there is a point on that section at which the derivative (slope) of the curve is equal to the "average" derivative of the section.
The mean value theorem can be used to prove Taylor's theorem, of which it is a special case.
Thus the Mean value theorem says that given any chord of a smooth curve, we can find a point lying between the end-points of the chord such that the tangent at that point is parallel to the chord.
en.wikipedia.org /wiki/Mean_value_theorem   (821 words)

 mean - definition by dict.die.net
Note: Mean is sometimes used in the formation of compounds, the sense of which is obvious without explanation; as, meanborn, mean-looking, etc. Syn: Base; ignoble; abject; beggarly; wretched; degraded; degenerate; vulgar; vile; servile; menial; spiritless; groveling; slavish; dishonorable; disgraceful; shameful; despicable; contemptible; paltry; sordid.
Mean distance (of a planet from the sun) (Astron.), the average of the distances throughout one revolution of the planet, equivalent to the semi-major axis of the orbit.
Mean sun, a fictitious sun supposed to move uniformly in the equator so as to be on the meridian each day at mean noon.
dict.die.net /mean   (789 words)

 Learning Resources: Statistics: Power from Data! Calculating the mean
The mean of a numeric variable is calculated by adding the values of all observations in a data set and then dividing that sum by the number of observations in the set.
As was mentioned in the soccer tournament example, the accuracy of the approximation of the mean will depend on how close each of the girls is to the midpoint of her interval.
Therefore, the mean height of the 50 girls in Grade 10 is 164.5 cm.
www.statcan.ca /english/edu/power/ch11/mean/mean.htm   (1063 words)

 Mean or Expectation Value
The mean is often called the "expected value" or the "expectation value".
The mean value of the binomial distribution is a = np where n is the number of events and p is the probability for each event.
From the definition of the mean using a distribution function, the binomial mean is
hyperphysics.phy-astr.gsu.edu /hbase/math/mean.html   (403 words)

 Arithmetic mean - Wikipedia, the free encyclopedia
While the mean is often used to report central tendency, it may not be appropriate for describing skewed distributions, because it is easily misinterpreted.
The arithmetic mean is greatly influenced by outliers.
The arithmetic mean of those rises is 10 %, but since the stock rose by $5.1 in 2 years, an average of 8.1 % would result in the final $35.1 figure [$30(1-10 %)(1+30 %) = $30(1+8.1 %)(1+8.1 %) = $35.1].
en.wikipedia.org /wiki/Arithmetic_mean   (850 words)

The mean value theorem states that under the specified hypotheses, there is a point in the interval of interest such that the slope of the tangent line at that point is equal to the slope of the secant line connecting the two endpoints of the graph of the function.
In other words, the average rate of change of the function f on the interval [a, b] is equal to the instantaneous rate of change of the function f at some point c in (a, b).
To find the value of c given in the Mean Value Theorem, we need to find a tangent line to the curve that has the same slope as the secant line.
www2.umassd.edu /temath/TEMATH2/Examples/MeanValueTheorem.html   (1370 words)

 How to Calculate Geometric Means
A geometric mean, unlike an arithmetic mean, tends to dampen the effect of very high or low values, which might bias the mean if a straight average (arithmetic mean) were calculated.
Because of how geometric mean is calculated, the precise substitution value generally does not appreciably affect the result of the calculation, and ensures that all the data remains usable.
For example, to calculate the geometric mean of the values +12%, -8%, and +2%, instead calculate the geometric mean of their decimal multiplier equivalents of 1.12, 0.92, and 1.02, to compute a geometric mean of 1.0167.
www.buzzardsbay.org /geomean.htm   (2931 words)

 Mean, Variance and Distributions
Two measures of the prospects provided by such a portfolio are assumed to be sufficient for evaluating its desirability: the expected or mean value at the end of the accounting period and the standard deviation or its square, the variance, of that value.
In addition, it is assumed that the values are drawn from a sample distribution taken from a larger population., and that the variance and standard deviation of the population are to be estimated.
where p(x) is proportional to the probability that the actual value will equal x; ev and sd stand for the expected value and standard deviation, respectively, of the distribution, and nd is the deviation of x from ev in standard deviation units.
www.stanford.edu /~wfsharpe/mia/rr/mia_rr1.htm   (3358 words)

 How to Calculate the Mean Value
The mean is just the average of the numbers.
The mean is equal to 330 ÷ 15 = 22
The mean is equal to 12 ÷ 5 = 2.4
www.mathsisfun.com /mean.html   (164 words)

 The Mean Value Theorem
Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.
I expect that in your textbook the conditions given for the Mean Value Theorem are either that "f(x) is differentiable for all x in [a,b]" or that "f(x) is differentiable for all x in (a,b) and continuous for all a in [a,b]".
The conclusion of the Mean Value Theorem is that somewhere on the curve between P and Q there is a point where the tangent line is parallel to the line joining P and Q. The first coordinate of this point is the number "c" in your problem.
mathcentral.uregina.ca /QQ/database/QQ.09.05/candace2.html   (371 words)

The Mean Value Theorem is used to prove many of the theorems and properties developed in Calculus.
Rolle's Theorem is a simplified version of the Mean Value Theorem and is used to prove it.
Geometric interpretation of the Mean Value Theorem: Where the theorem applies, there is a value of c on the interval (a,b) where the tangent line to the function at x = c is parallel to the secant line through the points on the curve at x = a and x = b.
www-math.cudenver.edu /~rbyrne/online/140w11.htm   (479 words)

 What is a P value?
The P value is a probability, with a value ranging from zero to one.
If the P value is 0.03, that means that there is a 3% chance of observing a difference as large as you observed even if the two population means are identical.
You happened to randomly obtain larger values in one group and smaller values in the other, and the difference was large enough to generate a P value less than the threshold you set.
www.graphpad.com /articles/pvalue.htm   (2330 words)

This book takes a comprehensive look at mean value theorems and their connection with functional equations.
Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane.
Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
www.worldscibooks.com /mathematics/3857.html   (123 words)

 Mean, Mode, Median, and Standard Deviation
Notice that the mean value is not a value of the sample.
The mean is influenced by outliers while the median is robust.
The mean, mode, median, and trimmed mean do a nice job in telling where the center of the data set is, but often we are interested in more.
www.ltcconline.net /greenl/courses/201/descstat/mean.htm   (865 words)

 Mean (DSP Blockset)
The Mean block computes the mean of each column in the input, or tracks the mean values in a sequence of inputs over a period of time.
When the Running mean check box is selected, the block tracks the mean value of each channel in a time-sequence of M-by-N inputs.
When the block is reset for sample-based inputs, the running mean for each channel is initialized to the value in the corresponding channel of the current input.
www.weizmann.ac.il /matlab/toolbox/dspblks/mean.html   (725 words)

 The Mean Value Theorem
Before we discuss the Rolle’s theorem and the mean value theorem, we will begin by the following theorems on which our subject is based.
Then there are numbers a and b in that interval such that f(a) is the maximum value of f and f(b) is the minimum value of f on I.
Geometrically, the mean value theorem says that if the graph of a continuous function has a tangent (which is not vertical) between two points A and B, then there is at least one point at which the tangent is parallel to the line
library.thinkquest.org /C006002/Pages/The_Mean_Value_Theorem.htm   (436 words)

 Random Processes: Mean and Variance
Finding the average value of a set of random signals or random variables is probably the most fundamental concepts we use in evaluating random processes through any sort of statistical method.
In this case we must estimate the mean through the time-average mean, discussed later.
The expected value of the sum of two or more random variables, is the sum of each individual expected value.
cnx.org /content/m10656/latest   (1036 words)

 mean - Definitions from Dictionary.com
mean well, to have good intentions; try to be kind or helpful: Her constant queries about your health must be tiresome, but I'm sure she means well.
Mean, low, base, sordid, and vile all refer to ignoble characteristics worthy of dislike, contempt, or disgust.
A number or quantity having a value that is intermediate between other numbers or quantities, especially an arithmetic mean or average.
dictionary.reference.com /browse/mean   (1987 words)

 Calculus I (Math 2413) - Applications of Integrals - Average Function Value   (Site not responding. Last check: 2007-10-10)
So, the average value of this function of the given interval is -1.620993.
So, in this case the average function value is zero.  Do not get excited about getting zero here.  It will happen on occasion.  In fact, if you look at the graph of the function on this interval it’s not too hard to see that this is the correct answer.
Mean Value Theorem that we saw in the Derivatives Applications chapter.
tutorial.math.lamar.edu /AllBrowsers/2413/AvgFcnValue.asp   (380 words)

 The Mean Value Theorem - HMC Calculus Tutorial
The Mean Value Theorem is a generalization of Rolle's Theorem:
This is formalized in the Mean Value Theorem.
The Mean Value Theorem is behind many of the important results in calculus.
www.math.hmc.edu /calculus/tutorials/mean_value   (404 words)

 Rolle's and Mean Value Theorems
The Mean Value Theorem (MVT, for short) is one of the most frequent subjects in mathematics education literature.
(The Mean Value Theorem claims the existence of a point at which the tangent is parallel to the secant joining
Both Rolle's and the Mean Value Theorem are statements of pure existence.
www.cut-the-knot.org /Curriculum/Calculus/MVT.shtml   (721 words)

 The Mean Value Theorem
The answers are "yes", "of course", and "yes" (this is the first derivative test), but ALL of these answers depend on a theorem called the Mean Value Theorem (MVT).
The Mean Value Theorem says that there is a point c in (a,b) at which the function's instantaneous rate of change is the same as its average rate of change over the entire interval [a,b].
At x = 0, the value of the derivative is 1.
oregonstate.edu /instruct/mth251/cq/Stage7/Lesson/MVT.html   (603 words)

 Visual Calculus - Mean Value Theorem   (Site not responding. Last check: 2007-10-10)
Objectives: In this tutorial, we discuss Rolle's Theorem and the Mean Value Theorem.
We look at some applications of the Mean Value Theorem that include the relationship of the derivative of a function with whether the function is increasing or decreasing.
Drill problems on using the Mean Value Theorem.
archives.math.utk.edu /visual.calculus/3/mvt.3/index.html   (271 words)

 The Mean-Value Theorem
The Mean Value Theorem is one of the most important theoretical tools in Calculus.
In fact, the Mean Value Theorem can be stated also in terms of slopes.
This does not contradict the Mean Value Theorem, since f(x) is not even continuous on [-1,1].
www.sosmath.com /calculus/diff/der11/der11.html   (243 words)

 mean :: Functions (MATLAB Function Reference)
M = mean(A) returns the mean values of the elements along different dimensions of an array.
mean(A) treats the values along the first non-singleton dimension as vectors, returning an array of mean values.
is a column vector containing the mean value of each row.
www.mathworks.com /access/helpdesk/help/techdoc/ref/mean.html   (110 words)

 Calculus I (Math 2413) - Applications of Derivatives - The Mean Value Theorem   (Site not responding. Last check: 2007-10-10)
Now, to find the numbers that satisfy the conclusions of the Mean Value Theorem all we need to do is plug this into the formula given by the Mean Value Theorem.
Here are a couple of nice facts that can be proved using the Mean Value Theorem.  Note that in both of these facts we are assuming the functions are continuous and differentiable on the interval
 in the interval and this is exactly what it means for a function to be constant on the interval and so we’ve proven the fact.
tutorial.math.lamar.edu /AllBrowsers/2413/MeanValueTheorem.asp   (511 words)

 Mean Value Theorem
This is an applet to explore one of the most important theorem in calculus: the mean value theorem.
Once you finish with this tutorial you might want to solve problems related to the mean value theorem.
You can adjust the position of the tangent such that the values of the slopes of the two lines are as close as possible.
www.analyzemath.com /calculus/MeanValueTheorem/MeanValueTheorem.html   (270 words)

 The Area Problem and the Definite Integral
The Mean Value Theorem implies the existence of
This is known as the First Mean Value Theorem for Integrals.
The point f (c) is called the average value of f (x) on [a, b].
www.sosmath.com /calculus/integ/integ04/integ04.html   (305 words)

 Mean - Wikipedia, the free encyclopedia
The mean number of legs is going to be less than 2, because there are amputees with one leg or no legs, but no people with more than two legs.
An unweighted mean can be turned into a weighted mean by repeating elements.
This connection can also be used to state that a mean is the weighted version of an unweighted mean.
en.wikipedia.org /wiki/Mean   (1373 words)

 Intermediate Mean Value Theorem
It is useful in many areas of science to be able to find out not just the mean value of a function, but also to glean some idea of the absolute size of it too.
It is clear that the mean of two numbers could be zero, but the size, which is more often called the norm, of two numbers cannot.
Although the mean value is, perhaps, more intuitive and physically appealling, it is the RMS value which arises more frequently in applications.
metric.ma.ic.ac.uk /integration/applications/imvt/index.html   (342 words)

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