Tagged Questions

The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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In what sense is the “average” of $sin(x)$ equal to 0?

I think it makes intuitive sense that if a phenomenon is described by simple sinusoidal oscillation, it is "on average" equal to its midrange, but I think I failed in trying to make that statement ...
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One number to represent the percent changes of multiple numbers

Question: Is there a way to represent the total percent change of multiple numbers (make it into one number that represents change) that isn't just the percent change between the first and last number ...
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Probable minimun of a set having only Maximum, Average and the number of values

I have a data set in which I am given the number of values, the average and the max, how can i work out the probable min value? Thanks
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Functions like EWMA

I have a problem in which a threshold triggers an event. I want to estimate that threshold dynamically as I get more information progressively. Exponentially Weighted Mean Average is one such ...
120 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
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Average distance to the closest neighbor

Suppose that 3-dimensional space contains countably infinite number of randomly positioned particles (points), on average $1$ particle per a unit of volume. Their distribution is homogeneous and ...
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How to calculate the average distance between two points in concentric annuli

I tried to solve this analytically but gave up and ran a simulation. I would still like to know if it can be done explicitly. Consider a circle radially divided into 'zones', so say zone 1 is the ...
Suppose you have a sequence $a_{1}, \dots, a_{n}$ and another sequence $b_{1}, \dots, b_{m}$, where $n$ and $m$ may differ. I want to know whether the difference between the arithmetic means of these ...