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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6
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0answers
201 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
votes
0answers
290 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
votes
0answers
56 views

Compute average and maximum value of a field over a streamline

I'm working on a code solving a set of PDEs. I have a vector field, $\vec{v}(x,\theta,z,t)$ (it's a velocity) and a scalar field, $c(x,\theta,z,t)$. I have a $2\pi$-periodicity in $\theta$. The ...
2
votes
0answers
70 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
votes
0answers
58 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
26 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
votes
0answers
207 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
votes
0answers
215 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
votes
0answers
429 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
vote
0answers
28 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 ...
1
vote
0answers
35 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 ...
1
vote
0answers
46 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
vote
0answers
59 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
vote
0answers
20 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
vote
0answers
66 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
vote
0answers
305 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
vote
0answers
31 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
vote
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
vote
0answers
65 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
vote
0answers
48 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
vote
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
vote
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
votes
0answers
4 views

Compute mean of a set from a biased sample

I want to compute the average of an unknown set $S$ containing real numbers. I can take arbitrary large number of samples from $S$, but the samples are not uniform, meaning that some numbers are ...
0
votes
0answers
39 views

About Bayesian formula and rating system

I'm building a scoring system with score from 0 to 5) and I would like to sort products according to the number of reviews and their scores. After some research on the Internet I have found two ...
0
votes
0answers
12 views

How does an increase in the order count in a conditional mean model affect the model?

How does an increase in the order count in a conditional mean model affect the model ,especially the effect on its filtering capacity, smoothness, lag ; while also its forecasting ability. By ...
0
votes
0answers
14 views

Unweighted Mean of Percentages

I have come across an interesting problem, which I'm sure there must be a standard solution to, but lots of Googling hasn't yielded much (which may mean I'm well off track...). I am trying to ...
0
votes
0answers
13 views

Average Cycle per Instruction

We have two different computers with the same instruction set. There are three classes of instructions (A, B, and C) in the instruction set. Computer M1 has a clock rate of 80 MHz and Computer M2 has ...
0
votes
0answers
22 views

The use of Weighted arithmetic mean to determine the extent to which the data correspond

I don't know when I can ask such question, because it is not a completely mathematic question. I have a text and a topic (single word). I want to check how much this text corresponds to the topic. ...
0
votes
0answers
31 views

find the no. of wagons need to be attached

The speed of an engine is proportional to the square root of the number of wagons attached to it. Without any wagons attached to it the speed of the engine is 60km/hr. With 16 wagons attached to it ...
0
votes
0answers
27 views

Problem of EOQ under conditions of uncertainty

I have solved the following problem for one half. Please help me to solve it full. A restaurant offers, at noon, only one menu at a fixed price of Euro 15. The cost of each meal is 12 Euros. From the ...
0
votes
0answers
75 views

Average and Standard Deviation for Angular Values

I'm trying to characterize an inexpensive accelerometer that provides (roll, pitch, yaw) values by generating basic running statistics (mean and standard deviation). But I'm unfamiliar with ...
0
votes
0answers
38 views

What is this called specifically?

Imagine you take a radius from the center of the shape, you add up all of the lines as it rotates 360 degrees. The radius is measured from its point of rotation, like (0,0) in Cartesian coordinates,to ...
0
votes
0answers
33 views

Problem calculating the average power of a vector?

I am calculating the average power of a vector. I would like to compare the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. Thank ...
0
votes
0answers
25 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
votes
0answers
32 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
votes
0answers
24 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
votes
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
votes
0answers
79 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
votes
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
20 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
votes
0answers
94 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
votes
0answers
50 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
votes
0answers
33 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
votes
0answers
20 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
votes
0answers
66 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
votes
0answers
97 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
43 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
votes
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
votes
0answers
19 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
votes
0answers
27 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 ...