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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2
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1answer
52 views

Zonal averaging of partial derivatives

Given a quantity $Q(x,y,t)$, the zonal average operator $[Q] = \frac{1}{2\pi}\int_0^{2\pi} Q\:\mathrm{d} \lambda$, and zonal anomaly $Q^\star$ such that $Q = [Q] + Q^\star$, my text book says that ...
1
vote
1answer
52 views

CAGR, log of negative numbers

I am trying to calculate the Compound Annual Growth Rate (CAGR) of a number of companies using the Geometric mean of the annual growth of their EPS. Some of the EPS values are negative(loss making) ...
1
vote
1answer
36 views

Difference between $\sum_{i=1}^{k}{\frac{s_i}{kn_i}}$ and $\frac{\sum_{i=1}^{k}{s_i}}{\sum_{i=1}^{k}{n_i}}$

I am getting confused at how to calculate the average probability. Suppose we repeat a kind of binary survey $k$ times each of which was done on a completely separate sample group. For each $i^{th}$ ...
6
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0answers
193 views

What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
4
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0answers
270 views

Average transformation matrix?

I have several estimates of the transformation matrix between two planes and some values that give some indication of the error involved in the estimate. How can I use this information to gain the ...
2
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0answers
67 views

Have averages, need variance

I have a large spreadsheet, generated by a colleague, that contains the results of $E$ experiments. For each experiment, he calculated the average of $M$ measurements. I need the calculate the ...
2
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0answers
57 views

The angle of an average rotation is $126.5^\circ$?

In the paper "Applications of Quaternions to Computation with Rotations" by Eugene Salamin, 1979 (click here), they get 126.5 degrees as the mean value of the rotation angle of a random rotation (by ...
2
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0answers
24 views

Inference the time a process would take depending on the number of threads

I have several datasets consisting on: Number of threads n Start process time t1 Stop process time ...
2
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0answers
159 views

How can you calculate actual values when all you have is rolling averages?

Let's say you have a set of data that is rolling 6 month averages of the actual monthly data. Good data collection would mean you saved the actual values and then calculated the rolling averages, but ...
2
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0answers
206 views

Exponential average of logs

I'm working on a sound recognition algorithm where an "exponential moving average" is used for "adapting" to sound levels. It turns out that taking an average of logs works better than simple sums ...
2
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0answers
409 views

How can I compare two averages of imperfect measurements, with their std. deviations?

I have a process by which I measure the times it take to do something, (run some code), and this time varies, a lot. I'm trying to optimize this code, making small changes that sometimes have small ...
1
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0answers
38 views

Finding possible numbers to yield a certain arithmetic mean (average)

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that: the arithmetic mean will be calculated from 20 integer numbers, each having a ...
1
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0answers
48 views

Deal or No Deal: Arithmetic, Median or Geomtric mean?

I'm trying to decide which type of mean is best to use when playing Deal or No Deal (in terms of comparing it with the Banker's offer). I realise the standard answer would be the arithmetic mean, but ...
1
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0answers
19 views

Estimator of Absolute Error?

Given $X \sim B(n, p)$, we know that $\hat{p} = X / n$ is the obvious estimator for unknown parameter $p$, and the following quantity $$\frac{\hat{p}(1-\hat{p})}{n-1}$$ has the property that its ...
1
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0answers
65 views

Game of bullets

Lets say with have a game with 10 targets. In each turn the participant shoots X number of different and random targets, where X is a random whole number between 0 and 10 (included). Game ends when ...
1
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0answers
199 views

Bar Mean vs Bracket Mean

I know that the standard representation for the average of a data set: $$ \bar{x} = \frac{1}{N} \sum_{i}^N{x_i} $$ I have also ran into an average denoted as $\langle x \rangle$. This notation is ...
1
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0answers
30 views

Is $x_1^{\alpha_1} + \dotsb + x_n^{\alpha_n}\geq x_1^{h/n}\dotsb x_n^{h/n}$ an example of power means?

I learned here that there is a relation between weighted means of the form $x_1^{\lambda_1}\dotsb x_n^{\lambda_n}$ and $(\lambda_1 x_1^r + \dotsb + \lambda_nx_n^r)^{1/r}$, namely that the former is ...
1
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0answers
61 views

Difference between $\frac{1}{n} \sum_{i=0}^n \frac{b_i}{a_i+b_i}$ and $\frac{\sum_{i=0}^n b_i}{\sum_{i=0}^n a_i + b_i}$

Consider scenario like this: each user can add movies. each user can rate movies he added. I want to know how many movies average user has unrated (as in average percentage). Let's translate this ...
1
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0answers
61 views

How to measure the time-decayed rate of independent event

I have events arriving in a software system at a variable rate. Imagine these events are, say, hits on a website. I'd like to periodically report on the rate of arrival of events over a number of ...
1
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0answers
46 views

Deconvoluting linear combinations of unknown distributions

Summary I am trying to deconvolute the distribution $T(x)$ of a population's $x$ parameter into sub-distributions ($P(x)$, $Q(x)$, $R(x)$ ...), of which I don't know the form (only that they have ...
1
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0answers
54 views

Taking averages

Suppose I have a function $f(\theta)$ that is a function of the angle $\theta\in [0,2\pi)$. Why is the average of $f$ over a large collection of randomly oriented objects: $$\int f(\theta)\sin ...
1
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0answers
29 views

Dynamic Light Scattering

In DLS does the combination of the Time Average and Ensemble Average give a better statistical average than the results shown by each case considered separately ?
0
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21 views

Economics Marginal Cost and Average Cost

I am in Computer Engineering but this year the university gave me choice for two electives with one being Psychology and the other Economics...So this being my first economics course I am really ...
0
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0answers
22 views

Mean values using eigenvalues - how?

I thought the definition of the average value of $f(x)$ was $f* = \frac{1}{T}\int_0^T f(t)dt$ How do I get from this definition to the definition of the mean value of a function in terms of ...
0
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0answers
18 views

Volume of a Part of a Triangular Prism Enclosed in a Sphere

I'm having trouble finding the volume of the shaded prism. I know how to calculate the volume by extending the height of this prism to create a triangular based pyramid, but I cannot get the same ...
0
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0answers
9 views

Average unused capacity of three capacity units

Let's say that there are 3 capacity units that have the following maximal capacities: ...
0
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0answers
24 views

Average minimum distance

Let $\mathbf{u} =\begin{bmatrix}u_1 & u_2 & \dots & u_N \end{bmatrix}^T$ and $\mathbf{v} = \begin{bmatrix} v_1 & v_2 & \dots & v_N\end{bmatrix}^T$. All the elements of ...
0
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0answers
26 views

Find spikes in data

I have some datasets and I need to find spikes in them. Imagine the data looks like trading data. If the spike is big enough, I need to log it, otherwise, proceed in the analysis. I tried with a ...
0
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0answers
71 views

How to prove the integral function with cosine is increasing

Prove that the following function is an increasing function on $x\in (0,1)$ when $n\ge2$. $f(x) = \int_0^{\pi} \frac{1}{(1-2x\cos\theta+x^2)^n} d\theta$
0
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0answers
12 views

Averages of sets adding to a constant

... Wow, I really need to learn how to make titles that make sense... I have a group of users each submitting a set of numbers. This set of numbers always totals $S$. The overall set looks something ...
0
votes
0answers
18 views

Getting the average of a serie of values

I am trying to smooth out a serie of values that represents tempo values, depicted in blue. The data comes from a tempo detection algorithm that as you might have guessed is not the best in town, the ...
0
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0answers
92 views

Calculate the value based on the number of people who assess the sheep.

I explain my situation. I have 30 sheep producing milk and 10 different customers that assess drinking it. To determine which of sheep milk is the best I would like to figure out how to establish a ...
0
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0answers
47 views

Minimum sample size to obtain population mean?

Knowing the average of a population, how could I evaluate an expected sample average based on k_sample? Data Info: Variance and standard deviation: $\sigma^2= 0.18500975256337462$ ...
0
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0answers
32 views

Average of angles by minimizing the squared distance.

I understand the answer the general method to find the average of a set of angles given here. I am trying to understand an answer given on stackoverflow (by Nimble) stackoverflow which considers cases ...
0
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0answers
19 views

Average data output from randomized data input?

Apologies about the title, I am not sure exactly how to word it. Currently I am receiving data from a Bluetooth Low Energy peripheral (RSSI in dB). Even if both the receiving device and the ...
0
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0answers
58 views

How to find “approximate most common” value from a list of RGB values

I have about 50 equally sized photos of magazine covers, which I'm attempting to blend into one composite image that shows the "average" cover. Each of the covers has a single face on it, so the ...
0
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0answers
85 views

Average of an exponential over Dirichlet probability distribution on the (n-1)-simplex

Any idea how I can solve this integral for arbitrary integer $n$ ($n \geq 2$) with real non-negative coefficients $\{s_i\}_{i=1,..,n}$: $I(s_1,...,s_n):= \int_0^1 dx_1 ...\int_0^1 dx_{n}\,\, e^{ ...
0
votes
0answers
41 views

Doubt on an Adaptive algorithm used for Voice Activity Detection

Recently in the task of implementing a adaptive energy algorithm for VOICE ACTIVITY DETECTION ,i came across an algorithm which is working properly and well but the problem is i am not able to ...
0
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0answers
31 views

Predicting future use.

I am in need of a formula that I can use to predict future use of a specific unit. You can think of the unit as how much electrical current is flowing in a wire. It varies a lot during the course of ...
0
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0answers
17 views

Average of several harmonic means

I would like to know if it is possible to calculate the mean and the standard deviation for several harmonic means. More specifically, I have 20 harmonic means. And every harmonic mean was calculated ...
0
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0answers
24 views

Are there any side effects of changing an alpha value on an existing exponential moving average?

I am designing an adaptive smoothing filter using an exponential moving average. However, instead of using a fixed alpha value I would like to use an incrementally increasing alpha value so that the ...
0
votes
0answers
28 views

Does MACD have exact or approximate upper bound and lower bound?

A MACD is a difference between two moving averages, typically, 12-day Exponential Moving Average and 26-day Exponential Moving Average. With some stock prices, I observed that the range of there MACD ...
0
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0answers
17 views

is f-mean a general form for all well-behaved means?

Can one claim that all well-behaved means can be written in form of f-mean? I mean means like logarithmic, etc. wikipedia link
0
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0answers
46 views

About a special way to find the average waiting time to get a sequence

A friend of mine taught me the following question: You have a coin. When you toss it up, heads you note $1$, tails you note $0$. Then, tossing it up repeatedly, let's find the average waiting time to ...
0
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0answers
49 views

change in sampling results and sample size

I am working on a problem, I have an experiment that each sampling gives me a numerical result. I want to create once a baseline of results that will give me very meaningful results. after creating ...
0
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0answers
71 views

Turn any shape to circle

I'm looking at trying to calculate and re position 3d vectors to align in a new position to form a circle. I've achieved this already however only when all points are evenly distributed in the same ...
0
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0answers
495 views

Averaging equation?

Is there any name for following averaging equation and how does it work? $$ y_{i+1} = (1-\alpha)\times y_i + x_i $$ I'm using it to average a signal, but I'm not sure am I interpreting the results ...
0
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0answers
175 views

Need algorithm to take “max” of scores, but with “quality” weighting

I have an application where I get a small number of scores from medical tests (the same test repeated a few times) and I need to combine them. Normally the highest score would "win" in this ...
0
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0answers
53 views

Calculating score

I have a number of values, grouped by some category. For every category, I've calculated average and standard deviation. Now I want to calculate a score (say 1 to 1000) for every category. I don't ...
-1
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0answers
23 views

How do you find averages of equations?

I am trying to figure out how to find the average of an equation. How do you do this with an exponential equation specifically? The problem gave me the equation 3.6(1.06)^x. It wants me to find the ...