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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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The mean of the following expression:

Suppose a discrete random variable X takes on the values $0, 1, 2, ,n$ with frequencies proportional to binomial coefficients $\binom{n}{0}, \binom{n}{1},....,\binom{n}{n}$ Then the mean (m ) and the variance ($s_{2}$ ) of the distribution…
user405925
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Different approaches to calculate weighted means

I am currently calculating weighted means of the DBH and height of my forest inventory data. I used 3 different approaches to investigate this data: I used nested plots like so: The smallest circle includes only the smallest trees(< 22cm Diameter…
Lukas
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Change of mean for a standard normal variable

Beginning to learn a bit of probability theory and I'm a little confused with this one. I know that given a Standard Normal variable X $X \sim \mathcal{N}(0, 1)$, if $Y = X + c$ then $Y \sim \mathcal{N}(c, \sigma^2)$ Now if, $Y = aX+b $, is $Y \sim…
Newtt
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What Mean for Mean of Geometric Means

Having calculated the returns over limited but simultaneous time periods (geometric means) for several financial time series, I'd now like to calculate the mean return of them all combined. What mean should I use, arithmetic or geometric mean of all…
babelproofreader
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Sample mean: dependence

I have a question that is possibly more about language than math, but still it concerns me a lot. I understand that this question may irritate many (because it's stupid, and apparently because I am stupid too), but still I ask not to hate me too…
oopcode
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Interpretation of a generalized mean

I am looking for a nice interpretation of the quantity $M(x_1, \dots, x_N) = \max_{(i = 1, \dots, N)} c_i \cdot \min_{(i=1, \dots, N)} \frac{x_i}{c_i}$ where the $c_i$ are positive 'weights' and the $x_i$ are non-negative. The expression shares…
MKR
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Help with a (simple?) proof

I have the following problem: I want to prove under what conditions the value of a cell (e.g. 1 or a in the graphics) is the column mean (e.g. 1.5) plus row mean (2) minus the grand mean (2.5) like shown in the graphics above. This is true for some…
holistic
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Relationship between mean of square and mean of cube to square and cube

Say I have a quantity I am measuring in time $u=\bar{u}+u'$, where $\bar{u}$ is the mean value and $u'$ is the fluctuating value. How can I find the relationship between $(\bar{u})^2$, $(\bar{u})^3$ and $\overline{u^2}$, $\overline{u^3}$ in terms of…
testman7
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Is it legit to compute the mean of log values?

I have two vectors where each element represents a value log2 transformed. v1 = c(1.4, 2.1, 1.9) v2 = c(-1.2, -2.2, -1.9) I'd like to compute the mean of v1 and v2 to show that v1 has higher average abundance than v2. Can I simply compute the mean…
julio514
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Separability of Means

Consider a set of data: $$X = {x_1, x_2, ... x_n}$$ where $x_i$ is of the form: $$x_i = c + y_i$$ where c is a constant The arithmetic mean over $X$ is: $$\frac{(\sum_{i=1}^n x_i)}{n}$$ The arithmetic mean is also: $$\frac{(\sum_{i=1}^n c)}{n} + >…
Mediocre_student1217
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Is the arithmetic mean relation of two sets of numbers hold for geometric and harmonic means?

Let Aset= {a1,..an} and Bset={b1,..bn} be two sets of positive numbers. AM - arithemtic mean, HM - harmonic mean, GM - geometric meam If AM(Aset) >= AM(Bset) then GM(Aset) >= GM(Bset) ? If HM(Aset) >= HM(Bset) then GM(Aset) >= GM(Bset) ? If the…
Ami
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Geometric mean with negative numbers

I want a workaround for the geometric mean when the data contains negative numbers. I found this on Wikipedia, but it doesn't work if m is odd and there is an even number of data points. What should the correct formula be? where m is the number of…
Greg
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Statistics test question about a mean

The following question from a Statistics test does not make sense to me. Question: Data from the past 100 years show that rainfall during April varies randomly from day to day. Over that period the mean amount in the month has been 60 cm, with no…
Namra
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Calculating a Grade in a Class

Assume that a class has four categories for calculating grades - tests, final exams, projects, and homework. Assume that tests are $40\%$ of the class grade, final exams are $30\%$ of the class grade, projects are $10\%$ of the class grade, and…
user1850284
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Can the overall mean be higher than all subset means?

I am investigating averages and have split my set into three sections and have found that the overall (global) mean is higher than the means of each of the three sections. Is this possible?
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