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Questions tagged [means]

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. Reference: Wikipedia.

For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.

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Geometric mean of reals between 0 and 1

What is the geometric mean of all reals between $0$ and $1$? I was thinking over this, but could not come up with anything useful. Please help me out.
user1001001
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What happens if you repeatedly take the arithmetic mean and geometric mean?

Given two positive real numbers, $A$ and $B$, such that $A\leq B$, take the geometric mean, giving $A'$, and the arithmetic mean, giving $B'$. Repeat ad infinitum. My intuition tells me that, since both means give values between the two original…
Malcolm
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Is there a name for this "mean"?

We all know these means: $$GM = \sqrt[3]{xyz} $$ $$AM = \frac{x + y + z}{3}$$ $$QM = \sqrt{\frac{x^2 + y^2 + z^2}{3}} $$ Of course: $$GM \le AM \le QM $$ What about this one: $$XM = \sqrt{\frac{xy + yz + zx}{3}} $$ Does it have its name? Are there…
VividD
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Where is the Harmonic mean used?

There is a mean called Harmonic mean. http://dlmf.nist.gov/1.2#E19 I mostly see usage of arithematic mean and geometric mean. On the other hand, I have never seen the usage of Harmonic mean yet. In what kind of case, is the Harmonic mean used?
sevenOfNine
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mean of geometric means?

Biological samples are taken weekly, and their values are averaged each month using the geometric mean. Monthly geometric means for several years of data are thus available. I want to compute the "average" value for each month of the year over a…
plasticnavymike
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Is there an easier/analogous explanation of geometric mean, similar to that of arithmetic mean?

My simple understanding of arithmetic mean is that the arithmetic mean represents a "central point" (central tendency) where all others numbers converge as the accumulative linear distance from the left equals the accumulative linear distance from…
B Chen
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Arithmetic mean of geometric means

I am looking for a simple closed-form expression simplifying the sum (or average, if you prefer) of the geometric means of all subsamples $A\subset X$ of cardinality $|A|=k$ from a grand set $X$, \begin{equation*} \sum_{A\subset X:…
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Compelling example for the geometric mean?

Does anyone have a nice example where the solution is the geometric mean? There are nice examples where the solution is the harmonic mean; see, e.g., Arithmetic mean vs Harmonic mean An example similar to that (not rooted in geometry) would be…
max_zorn
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Geometric mean on negative numbers - work-around

The geometric mean defined as $$\text{Geometric mean}=\sqrt[n]{x_1\cdot x_2\cdots x_n}$$ is only defined for a positive inner product. A description and clarifications are in this question. Having negative numbers in a dataset can thus make it very…
Steeven
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How to generalize the Arithmetic geometric mean

Finding the AGM of two terms is well understood. Since both its Arithmetic and Geometric components can be generalised (identity for a single term, undefined for fewer), can the AGM also be generalised? I would assume yes and further assume identity…
hildred
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Are the Arithmetic, Geometric, & Harmonic mean part of a sequence of types of mean? If so, which types of mean would come next in the sequence?

To my understanding arithmetic mean income is influenced by people on high incomes more than medium and low incomes, Geometric mean income is equally influenced by people on high, medium, and low incomes, and Harmonic mean income is more influenced…
novice
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is the word 'mean' an uncountable noun

In math, is the word "mean" used only in singular form? Can it be used in plural form, like this: The means of DSW and SDA were 5.89±1.8 mm, and 12.37±4.09° respectively. Thanks very much :)
troysantos
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Equation relationship between the arithmetic mean, the geometric mean, and the harmonic mean of more than two numbers

Let $A$ be the arithmetic mean of set $s$, $G$ be the geometric mean, and $H$ be the harmonic mean. I know that when there are two terms in a set, $G=\sqrt{AH}$. However, is there an equation like this for when there are more than two terms? I…
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Knowing the arithmetic, geometric, and harmonic mean of a set, can I find the number of terms in the set? If not, what more information do I need?

Consider a set $a$ with $t$ terms. Knowing the arithmetic mean, the geometric mean, and the harmonic mean of $a$, could I somehow solve for $t$? If not, what more information would I need to know?
4yl1n
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What kind of mean is this?

I recently came across the following method of calculating, from what I understand, a special kind of mean. For 3 items: $\frac{\frac{a}{2} + b + \frac{c}{2}}{2}$ For 5 items: $\frac{\frac{a}{2} + b + c + d + \frac{e}{2}}{4}$ What kind of mean is…
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