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.
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How much less is the arithmetic mean than the max given the average deviation?
Given a finite (multi)set of elements $\{x_1, \ldots, x_n\}$ the arithmetic mean $\mathsf{AM}$ is less than or equal to the maximum element call it $\max$. In otherwords, $\mathsf{AM} \leq \max$. But ...
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What is a numerically practical and safe measure of dispersion of a data set?
I am using a moving average filter to calculate the average value of my sensor measurements. The window size is $N$. I am also using Welford's algorithm for a rolling window to calculate the variance ...
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How can I end up winning more often than losing if my per-game win probability is only $\sim 40%$?
Rules of the Game:
You play with a fair 6-sided die.
You choose a target number, for example: "2".
Then you repeatedly roll the die, one throw at a time.
If you roll a 2 at any point, the ...
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Defining the actual rate of expansion of a sequence of bounded sets w.r.t a reference point
Motivation: We wish to define the rate of expansion of sequences of bounded sets to answer the leading question of this paper ($\S3ドル.1). The current definition in $\S5ドル.1 of this paper does not ...
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Create joint ranking
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lets say we have some 10ドル$ things. these things have property1 and property2, and we rank those things by ...
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Calculating weighted growth rates of two indicies
I have two indexed yearly time series (Consumer Price Index and Average Salary Index).
My goal is to obtain weighted growth rate (per year) of these two with 40% given to the Consumer Price Index and ...
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Figuring how to calculate outliers in a customer data set
I have a dataset of customers and I'm trying to figure out at what point, based on the number of items you return, you have statistically returned "too much". The data set looks somewhat ...
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Where have people discussed "higher" arithmetic-geometric means?
The arithmetic-geometric mean of two nonnegative real numbers $x,y$ is obtained by taking their arithmetic and geometric mean
$$ a_1 = \frac{1}{2}(x + y), \quad g_1 = (xy)^{\frac{1}{2}} $$
and then ...