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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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Is there a way to generally transform a weighted arithmetic mean to a weighted geometric mean?

I was wondering under what general conditions and how it's possible to transform a weighted arithmetic mean to a weighted geometric mean. Assume there are positive weights $a_1,\dots,a_n$ that sum up to $1$ (i.e. $a_1+...+a_n=1$ and $a_i\geq0$…
Christian
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Solve for E(X) with ln function

So, I tried to compute the expected value of continous random variable X using an integral and the typical formula given here: $\mathbb{E}$(X)=$\int_{-\infty}^{\infty} x*f(x)) dx$ And I plugged a function in…
TheAverageAnne
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How to create n datasets of size N with same mean but different standard deviation?

I am looking to create 400 datasets of size 180 numbers with the same mean but a different standard deviation. Is there a way to do this other than trial and error? Possibly some way to automate this process? Thanks
user5241675
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Need 2 calculations explained

This is math 101 but I am struggling to fully comprehend the difference between these 2 calculations. I have 50 observations of the value of sales and volume of sales (in lbs). Price per unit = value/volume. If I calculate the price for each…
406LQE
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Which mean to calculate for a series of points (x,y)?

I have a series of points in space with $(x_i,y_i)$ coordinates. And I would like to represent the average/mean point of this series: --> Should I go for an arithmetic or a geometric mean of $x$ and $y$ coordinates ? Thanks a lot to answer to my…
Gab
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"Better" mean depending on sample size

I'm terribly sorry about this super noob math question, but I've been reading for a while now and don't seem to find a starting point. This is my problem: My samples have very variable sizes. I want to sort them by "best" mean, but having into…
Aylen
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The weighted average of weights will be smaller than will be smaller than the weighted mean in some cases.

Suppose I have $w_i>0$ and $x_i>0$ for $i=1,2,\ldots, n$. I know that, $$\sum_{i} w_i < \sum_{i} x_i \leq 1. \tag{1} \label{eq1}$$ Can I say that, $$\sum_{i} w_i w_i < \sum_{i} w_i x_i. \tag{2} \label{eq2}$$ Edit: I change the question as…
entropy
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The mean of four numbers is $12$. When the greatest number is removed, the mean becomes $9$. What number was removed?

Here's a question that I couldn't solve, apparently: The mean of four numbers is $12$. When the greatest number is removed, the mean of the remaining three numbers is $9$. What number was removed? Thanks so much if you can solve it! PS: You…
TECHron
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Do the Pythagorean means preserve the order among groups of observations?

I know that harmonic mean HM <= geometric mean GM <= arithmetic mean AM Thus, if I have two groups of observations such that AM of group 2 > AM of group 1 The smallest possible value of an observation is 1. Is is true that the same inequality holds…
Simone
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What is the median of the $6$ terms?

Can anyone help me with this? The problem seems quite simple, but I can't get the same answer as the answer sheet. My answer to this question is $9$, but the answer sheet is $54$. In a sequence of $6$ positive integers, each term after the first is…
learning
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Possibility of finding 3 distinct positive integers whose harmonic mean is an integer

Is it possible to find 3 distinct positive integers a, b, c such that the result abc/(ab + bc + ca) is also an integer?
Karri Chandrasekhar
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A very elementary problem that I want to see if its solvable or not

Here's the problem: I wrote this as part of a test I'm writing and I want to see if it's solvable or not.
Voldemort's Wrath
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What happens if there is no difference between the mean and the weighted mean?

I was wondering. What happens if there is no difference between the arithmetic mean and the weighted mean? Why would that happen?
Nathan Fleischman
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