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
251 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
428 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
120 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
54 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
39 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
190 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
33 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
63 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
74 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
681 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
266 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
512 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
15 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
14 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
24 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
28 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
13 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
20 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
18 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
41 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
22 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
39 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
357 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
44 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
143 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
113 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
26 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
69 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
60 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
41 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
13 views

Can distributions scale to any given time scale?

I am working with some colleagues to set up alerts based on call center data, and I feel that something is wrong with how it is currently being done, but I'm not sure what exactly, or how to explain ...
0
votes
0answers
16 views

How to determine a formula for an index of compliancy

I hope you will be patient with the inarticulate question of a non-mathematician. It's hard to get an answer when you don't even know how to ask the question. Here the contest: Let's say that I have ...
0
votes
0answers
5 views

Average discount give for product line

I have been out of school for entirely too long to remember how to build this equation. I am trying to calculate the average discount given for our entire product line, that is sold over 4 distinct ...
0
votes
0answers
20 views

What is the appropriate way to average a set of slopes?

I have a set of line slopes (output from linear regressions) and I'd like to combine them to yield some measure of the 'slope' of the set. However, simply taking the mean of the numbers doesn't make ...
0
votes
0answers
8 views

Another name for mode frequency

Is there another term for the number of times the mode number occurs in a list/array of numbers or 'the frequency of the mode' in a list/array of numbers? Apologies if this has been asked before - I ...
0
votes
0answers
9 views

Weighted Average Using Rankings

So I have this data and I've ranked each category for each person. The best being 1. I can average them , just add up and divide, but I need to weigh them. If I weigh them like normal: ...
0
votes
0answers
19 views

Determine contribution percentage

I'm trying to determine the individual category percentages once their weights have been applied. The easiest way to describe what I'm asking is to show my workings: ...
0
votes
0answers
10 views

Does (messing up) FIFO affect average cycle time?

I'm currently in the midst of a corporate class on process improvement and ran into the following situation: Workflow process containing several steps. No step is skipped or done out of order. ...
0
votes
0answers
24 views

Average number of $5$-card draws before all $52$ cards in a deck are drawn.

So an interesting question was brought to me today and I'm not sure how to formulate the equation to answer it. A person draws $5$ cards from a deck, writes the cards down, puts the cards back in the ...
0
votes
0answers
10 views

Multiple server queuing model

I have come across the following problem in one of my courses: Let's suppose a patient in a hospital is waiting to be picked by one of the two doctors available. The time till a new pacient arrives ...
0
votes
0answers
22 views

Weighted average of unit vectors

I am trying to determine the yaw (z) axis of a vehicle given a bunch of sensors, each of them subject to different kinds of error. This means I get a bunch of unit vectors for the z axis, expressed ...
0
votes
0answers
28 views

How to find the best-case and average-case number of comparisons performed by a comparison tree?

So I'm reviewing some material before a midterm tomorrow and I came across this question: ...
0
votes
0answers
54 views

Calculating the average case complexity for finding the maximum number in an array

Algorithm: Given a non empty array with $N$ Numerical values, the algorithm finds the location LOC and the maximum value MAX of the largest element of DATA. Initialize K:= 1, LOC:=1, ...