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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7
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0answers
264 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
466 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 ...
3
votes
0answers
132 views

Finding a summarizing vector for average angle calculation

Let $L$ and $R$ be two bags of positive vectors such that all vectors have length $k$. Define the distance $d_{avg}$ between the bags as the average pairwise angle between the vectors. Is is possible ...
3
votes
0answers
59 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 ...
2
votes
0answers
40 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
2
votes
0answers
203 views

Math Average Basics, Error % calculation, and Blood Pressure.

I saw on the Olympics once when they were doing scoring for team events, that on some events the judges would take each members performance, eliminate the highest and lowest members performances, and ...
2
votes
0answers
34 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...
2
votes
0answers
64 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
76 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
29 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
721 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
279 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
516 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
13 views

Geometric mean, harmoinc mean and loss functions

Consider a sequence $(x_i)_{i \in I}$ of real numbers indexed on a set $I$. The mode of the series is the minimizing argument for the $L_0$ loss $$ \text{mode}[ \; (x_i)_{i \in I} \; ] = \arg\min_{u \...
1
vote
0answers
11 views

Does Averaging the score from correlation across multiple variables yield a more accurate correlation score?

This may be a beginner question but I am making a application which I using to do correlation research to be used in financial markets. The application pulls in different data sources and compares ...
1
vote
0answers
30 views

What do attendance figures tell me about regularity? What does the average tell me about individual attendance?

Suppose I have a group of $N$ people, attending a series of $M$ events, and (for simplicity) let's assume the overall attendance happens to be the same at each event, say $A$ people (ranging between 1 ...
1
vote
0answers
25 views

Variance of exponential moving average

I'm not quite sure what the form for the rolling recursive variance should look like. I have that the recursive average is $m_t = \alpha x_t +(1-a)m_{t-1}$. Then would the rolling recursive variance ...
1
vote
0answers
32 views

Exponential smoothing and variance

I have a time series, let's denote it as $X_t$ (a series of prices). We exponentially smooth the data to obtain another time series, an exponential moving average: $EMA_t$. My question is how do I ...
1
vote
0answers
17 views

Confused by simple risk problem

I am having troubles understanding this basic problem and would like to see if anyone could help me out. I have two boxes: one red, one blue. Depending on what box I pick, I have the potential to ...
1
vote
0answers
20 views

Average Value of a Line Integral

I'm having quite a hard time calculating the average value of a line integral. Given the surface $f(x,y) = \sqrt{16 + 36y^{2/3}}$ and the curve $y = x^{3/2}$, I need to calculate the average value of ...
1
vote
0answers
29 views

Expected waiting time - simplified

I need some assistance with a calculation I'm trying to do. I have access to surgery waiting times data (date arrived, date completed) and I want to figure out the expected waiting time for a new ...
1
vote
0answers
39 views

Median of medians vs. single median

I have 10 sets. Each set corresponds to a user. Each set contains a different amount of floating point numbers. Each such number corresponds to a response time (of a user). Now I would like to ...
1
vote
0answers
15 views

Do I need to calculate the weighted average in these cases?

I'm aware of the concept of calculating a weighted average but the data I'm working with is confusing me. I couldn't find any similar examples when I did a search. Here's an example. We have a number ...
1
vote
0answers
19 views

Approximate values from point groupings

Say I am given a set of values: \begin{bmatrix}0.9&1.1&1&1.95&2&2.05&2.95&2.95&3.1&3\end{bmatrix} Is there a way I can get the 'center' or 'average' values 1, 2, ...
1
vote
0answers
29 views

Averaging speeds

I read the answer to this question: http://stackoverflow.com/questions/34794664/how-should-i-calculate-the-average-speed-by-road-segment-for-multiple-segments/34795821#34795821 Can anyone please ...
1
vote
0answers
23 views

Advise on Weight Function for statistical analysis needed

I'm doing a statistical analysis of an experiment I'm conducting, and right now I'm trying to define a proper methods for data mining. Please take a look at my problem: I'm doing a user research ...
1
vote
0answers
26 views

Calculating Weighted Averages – selecting a correct numerical scale for several variables

I have the following variables that i am going to use to calculate a weighted average: Variable Format Weight applied (out of 1) A Percentage 0.2 B Percentage ...
1
vote
0answers
37 views

Understanding the convolution as a weighted average to eliminate noise $ s(t) = \int x(a) w(t-a) da$

I was reading Yoshua's Bengio [book][1] on convolutional neural networks and it has small section that described/explains the convolution in the context of estimating the location of a spaceship with ...
1
vote
0answers
19 views

What kind of time series do I need?

I am trying to optimize a list of websites on which to purchase banner advertising using the following setup: For each banner ad impression I buy I am charged $0.001. When my ad is clicked it ...
1
vote
0answers
42 views

Matlab, Extracting Particular Values from an Excel File

If I have a table of values in Matlab ( here I have a 40k rows, and about a dozen columns), how can I read only particular values from each row? My goal is to extract some of the values from each row, ...
1
vote
0answers
23 views

Averaging Models in Excel

I am working in Excel and have two sets of data points that come up with a percentage for the likelihood of a recession. I am wondering what the best strategy would be to combine these data points? ...
1
vote
0answers
43 views

Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
1
vote
0answers
395 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 ...
1
vote
0answers
45 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 $\mathbf{...
1
vote
0answers
169 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
114 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
28 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
2k 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
38 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
79 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
70 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
61 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
42 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
23 views

Method used to calculate average time spent

I need to calculate the average time spent on a single article. My data set ranges from a few seconds up to an hour. Dataset Summary .png file I'm currently using mean to calculate the average but ...
0
votes
0answers
22 views

Aproximation for the variance (sum)

Given that we know The mean of a population $\tilde W(t) = \sum_{i=1}^{n}f_{i}(t)*W_{i}$ The variance of the population in the previous step $Var(0) = \sum_{i=1}^{n}f_{i}(0)*(W_{i}-\tilde W(0) )$ ...
0
votes
0answers
8 views

Weighted mean / average where you reward the lowest value - cost - distance

Best I've several weather-station (200), placed across the country (508 municipalities). Now, I would like to prescribe the weather info, e.g. temperature, to each of the municipalities of that ...
0
votes
0answers
38 views

How can I calculate accuracy of an estimate based on a subset of data?

For example, say I'm trying to determine the average number of steps taken in a day for a population of 100M people. I know the exact number of steps for a random 25M subset of the 100M group (2500 ...
0
votes
0answers
11 views

Normalize and Average weighted

Everyday I receive a data of three variables (neutral, negative and positive). ...
0
votes
0answers
23 views

Boosting v. weighted average

I have been watching an MIT online Artificial Intelligence lecture by Prof. Winston about boosting. The boosting technique uses complicated maths to combine the results from several weak predictors to ...
0
votes
0answers
27 views

Anyone have any good ideas on how to average 2D directions?

Directions, being a cyclical quantity (i.e. if you keep increasing the value, you'll eventually end up back where you started) can't be averaged out like regular numbers. For example, say I have 2 ...