Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [average]

Averages summarise a set of values in one way or another. Without further qualification it most commonly refers to the arithmetic mean, but other averages such as root-mean-square exist.

In its most general definition, an average is a summary of a set of values. Normally it refers to the arithmetic mean, but other means may be employed (geometric, harmonic, etc.) or a transformation may be applied before and after taking a mean (e.g. root-mean-square).

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Averaging compound interest rates is returning an unexpected result

Let's consider two stocks with the following prices for a three days period: Stock 1: day 1: 100 day 2: 105 day 3: 110 Stock 2: day 1:100 day 2:100 day 3:110 The increase percentage each time for stocks 1 and 2 are respectively: Stock 1: [5%…
Amine Hajyoussef
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Formula for "inverse" weighted average (smaller value gets higher weight)

This might be really simple, but I'm stuck. Suppose I have 3 triangles with areas A0, A1, A2. I want to compute a weighted average for these values. To do that, I divide each area by the sum of all areas. This way I obtain weights w0, w1, w2 such…
Beriol
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Finding mean of $n$ consecutive numbers using a shortcut

I am working on the following question: Let us say we have $n$ consecutive numbers labelled $x_1$ to $x_n$. I want to find the average of these. The quickest way to do this seems to be $$AVERAGE=\frac{x_1 + x_n}{2}\tag1$$ The other way to do this is…
Joebevo
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Averages and differences

A student asked me a question that I couldn't answer, and I said I'd find out. I set a problem which was, given a set of numbers, was the mean over 50 where the numbers are: 56, 42, 47, 59 and 48 The mean is 50.4. A student asked why it wasn't 52,…
Marc Stewart
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Mathematical average formula

For any mathematical average, the sum of how much larger than the average the numbers above are must equal the sum of how much smaller than the average the numbers below are. Mathematical averages are usually calculated by adding all the numbers up…
Yukang Jiang
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Weights of simple moving average are not adding up to one

This is the definition of linear filter from a book I am reading: A second procedure for dealing with a trend is to use a linear filter, which converts one time series, $\{x_t\}$, into another, $\{y_t\}$, by the linear operation $$y_t = \sum_{r =…
Kocur4d
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Two methods of calculating new average from old average

I know that calculating the new average $a_{new}$ from the old average $a_{old}$ can be done in the following way (for uniform weights): Suppose the old average is based on $n$ elements. The old total is then $t_{old}=a_{old}\cdot n$. The new total…
Faceb Faceb
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I am stuck up with this simple problem related to averages.Please help me out in explaining the complete solution to this problem

I am stuck up with this simple problem related to averages. Please help me out in explaining the complete solution to this problem. Consider a class of $40$ students whose average weight is $40\ \mathrm{kg}$. $m$ new students join this class whose…
Roy
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Removing my averages

thanks for your time and apologies if this is far too simple for this group. I am trying to remove my average from a total average. Meaning: The total average for a subset of data is 55. I am 29% of this subset and my average is 52. If I were…
user354333
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Is this some known mathematical concept?

I was thinking about a way to do a "weighted average" (that's what I call it, could be dead wrong) of a variable $x$ defined for a given range $x_1\leq x\leq x_N$, weighted by an always positive function $f(x)$. I came up with the following…
Gabriel
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What is this average called?

What is this average called? I tried Googling it but couldn't find anything about it. It's something between an arithmetic mean and a geometric mean, by which I mean you iterate both averages for two numbers until they converge. To find that average…
Michel Rouzic
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Time to extinction

Suppose that a population has a rate of extinction equal to $k \exp({-\epsilon N})$ where $\epsilon$ and $k$ are constant and $N$ is the population size. This also means that the time to extinction is given by $k \exp({\epsilon N})$. By the way,…
r_31415
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Average distance from center to random point in rectangle

I need to find average squared distance from center in rectangle. One edge is 2, other one is 1. On my understanding I need to find $$E[X^2+Y^2]$$ So I got $$\int_{-1}^{1}\int_{-0.5}^{0.5}x^2+y^2dxdy$$ Is it ok, or I am missing something?
dmsmar
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Correct way to get average price

probably a basic question for a lot of you guys, but it was a subject of a friendly debate at my work earlier - needless to say none of the involved were accountants. In short, we are thinking about which is the proper way to get the average price…
picus
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How can I find the mean score when using the following Likert scale

I have some quantitative data in the form of Likert scale, and I would like to obtain the mean score for each question. I am using +2.0 = ‘Strongly Agree’, +1.0 = ‘Agree’, 0.0 = ‘Not Sure’, -1.0 = ‘Disagree’, -2.0 = ‘Strongly Disagree’. If I had 8…
Justin
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