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
36 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
2
votes
1answer
31 views

Choosing two sets of values with the least difference between the averages of the sets

This is probably a simple Combination problem but I can't think of how to solve it in LibreOffice. I run multiplayer games along with seven of my friends, on two teams of 4 players each, for a total ...
2
votes
1answer
243 views

Average distance from center to random point in rectangle

I need to find average squared distance from center in rectangle. One edge is 2, other one is 1. On my understanding I need to find $$E[X^2+Y^2]$$ So I got $$\int_{-1}^{1}\int_{-0.5}^{0.5}x^2+y^2dxdy$...
2
votes
2answers
223 views

Calculating mean (Average) of vector

I'm trying to calculate PCA (Principle component analysis) and part of the equation is to calculate the mean of a vector $v$ and subtract each element of $v$ by it's mean. However, is this in column ...
2
votes
1answer
63 views

Are the $L^p$ norms ordered by $p$?

A question left over from this post is: Are the $L^p$ norms ordered by $p$ like the power means are?
2
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1answer
230 views

Maximum and minimum of weighted sum

For $w_i\ge 0$ and some constants $\alpha_i , i=1,...,n$, what is the maximum and minimum of $\sum_{i=1}^{n}\alpha_i w_i$ subjected to $\sum_{i=1}^{n}w_i=1$? Intuitively, I put all weight on the ...
2
votes
1answer
314 views

Arithmetic, Geometric, Harmonic Means

There are situations in which just one of the arithmetic, geometric, and harmonic means are appropriate to use an the other two are meaningless. Is there any situation which more than one of these ...
2
votes
1answer
94 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 ...
2
votes
2answers
2k views

How to calculate weight of positive and negative values.

We have used formula formula to calculate weight as, $$ w_1 = \frac{s_1}{s_1 + s_2 + s_3};$$ $$ w_2 = \frac{s_2}{s_1 + s_2 + s_3};$$ $$ w_3 = \frac{s_3}{s_1 + s_2 + s_3};$$ However, their is ...
2
votes
1answer
822 views

Average delta value of a sequence of $N$ $8$-digit numbers

Given a sequence of $N$ $8$-digit numbers, how to calculate the average delta value, thanks.
2
votes
1answer
212 views

Average number of rolls of die to see each side at least once [duplicate]

Possible Duplicate: A Question About Dice You have a weighted n-sided die. Every side of the die is weighted differently where side n1 has a weight of w1, n2 has a weight of w2, ... Estimate ...
2
votes
1answer
5k views

Average, standard deviation and min/max values

I'm analzying a computer science paper and just found in the experimental setup the following statement: Average (standard deviation) of number of files per peer: 464 (554) Min - max number of files ...
2
votes
1answer
430 views

Error Metric which incorporates both mean & standard deviation of data in euclidean space

For simplicities sake (the actually problem is more complex)...Let say I have a set of n 3d points, whose position move over time. For all pairs, I have calculated the mean and standard deviation of ...
2
votes
1answer
147 views

Fréchet mean between points in $\mathbb{R}^3$

Let $X$ be a set of $n$ points in $\mathbb{R}^3$ and $f_m$ be the Fréchet mean, i.e.: $$ f_m= \arg \min_{p \in M} \sum_{i=1}^n w_id^2(p,x_i) $$ where $(\mathbb{R}^3,d)$ is a complete metric space, $...
2
votes
1answer
364 views

Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
2
votes
1answer
440 views

Calculating kWh from multiple watt readings

I have a file which contains watt readings for various times throughout the day. A reading is stored roughly every 6 seconds. ...
2
votes
0answers
43 views

What is the average maximum value of a set of random numbers? [duplicate]

Let $a_1, a_2, a_3, \ldots, a_{10}$ be ten randomly chosen real numbers in the interval [0,1]. Let $m$ be the maximal value out of these 10 numbers. What is the expected value of $m$? (i.e. If i ...
2
votes
1answer
40 views

Average velocity of fluid flow

Washburn equation for fluid flow in horizontal capillary is given by : $\frac{dL}{dt} = \frac{γR}{4µL}$ Find the time dependencies of length of travel, $L(T)$ and average velocity. I can find the ...
2
votes
1answer
168 views

How to calculate the average distance between two points in concentric annuli

I tried to solve this analytically but gave up and ran a simulation. I would still like to know if it can be done explicitly. Consider a circle radially divided into 'zones', so say zone 1 is the ...
2
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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
1answer
39 views

Is tossing a die in 10 consequent days an ergodic process?

IT maybe an elementary question but I'm totally new to the concept. In Wikipedia, ergodicity is defined as follows: In statistics, the term describes a random process for which the time ...
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
2answers
64 views

Average Growth Rate for Year 1 across 5 groups

Lets suppose that I am measuring the total number of online visitors to 5 websites on a monthly basis. I have this data for the months of Jan - Dec. What I want to understand is "What is average ...
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
1answer
210 views

Does “Expected Absolute Deviation” or “Expected Absolute Deviation Range” exist in stats and have another name?

So everyone is familiar with Variance and Standard Deviation from high school, but it seems no one has any familiarity with a philosophical justification for such weird, seemingly arbitrary measures. ...
2
votes
1answer
70 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 ...
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
2answers
63 views

Rate of appearance of digits 7 and 8 in a given sequence

This is from Arnold's Mathematical Methods of Classical Mechanics: let us consider the sequence $$ 1,\ 2,\ 4,\ 8,\ 1,\ 3,\ 6,\ 1,\ 2,\ 5,\ 1,\ 2\ \ldots $$ which consists of the first digits of the ...
2
votes
1answer
177 views

Rating System: Statistically significant with weighted entries

The title may be a bit confusing because I not exactly sure how to do/explain what I am after. I have judges rating an object on a score 1-100, where the majority of objects will in the range 85-95 ...
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
1answer
312 views

Estimating a sample mean using sub-sample means

we collect a lot of data on a daily basis via an API, and part of this data includes fields that represent sample means. Specifically, we get provided with a sample mean and the sample size, lets call ...
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 ...
2
votes
3answers
59 views

Determining the Average number of Attempts before a result occurs (using defined Probabilities)

I'm trying to solve this problem but I'm completely unsure of what sort of concepts/formulas/proofs I need in order to tackle it. I'm just lost on where to start. Here's an example story problem as it ...
1
vote
3answers
103 views

Is $\frac{a^2+b^2}{2}=c^2$ possible?

I am looking for an integer solution to the equation: $$\frac{a^2+b^2}{2}=c^2(a\neq b\neq c)$$ That is a square number that is the mean of two other square numbers, is this possible? And if so please ...
1
vote
5answers
185 views

How do you determine the “average” of a certain value?

I have checked out the Wikipedia article, but it's too complicated for me. Also, this definition: constituting the result obtained by adding together several quantities and then dividing this ...
1
vote
2answers
78 views

Finding one value from a mean.

7 boys have a mean height of 1.80m. Peter joins the boys and now the mean height is 1.75m. Find Peter's height.
1
vote
1answer
288 views

How long does it take to complete a sticker album?

We are collecing stickers in chocolate bars and whenever we open a bar we get a random new sticker. There are many different stickers and we try to collect them all. We open the first bar and get a ...
1
vote
1answer
2k views

Average distance between two random points in a square

A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square? For more general rectangle case, see here. The proof found there is ...
1
vote
2answers
388 views

How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?

Let $a$, $b$, and $c$ be positive real numbers such that $a+b+c = 1$. Then how to establish the following inequality? $$ (1-a)(1-b)(1-c) \geq 8abc.$$ My effort: Since $a+b+c =1$, we can write $$ (...
1
vote
2answers
35 views

Average $y$ from a range of $x$ in a parabola

Given a parabolic/quadratic formula such as $ax^2 + bx + c =y$, how do I get the average value of $y$ given a range of $x$ ($x_{min}$ to $x_{max}$). Real world example: if my formula represents the ...
1
vote
3answers
85 views

What is the expected value of this random number?

Suppose $a$ is a random number between 0 and 1 and suppose $b$ is a random number $\in (0,1)$ also. What is the expected value of $a^b$? (i.e. If I performed this operation $n$ times, what would be ...
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vote
2answers
40 views

Proving that mean KDR in a videogame is one

This is not related to schoolwork. A friend of mine challenged me to prove that the mean KDR (assuming players can only die at the hands of other players) must always be equal to one. I have gotten ...
1
vote
1answer
193 views

New Average with a number deleted

A set of consecutive integers were written down: $1, 2, 3, 4, 5, ... x-1, x, x+1, ... n-2, n-1, n$ One number, $x$, is deleted. The arithmetic mean of the remaining numbers is $602/17$. What does "$x$"...
1
vote
1answer
3k views

Average proportion for proportions with different denominators

Say I have an experiment in which subjects are asked to respond to some stimulus. Their responses are transcribed and coded, first as "Valid/Invalid", and then for the valid responses, "Correct/...
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vote
2answers
3k views

Statistic Missing Value [closed]

A professor has recorded exam grades for $30$ students in his class, $1$ of the $30$ grades is unreadable. The mean score on the exam was $82$, and the mean score of the $29$ available scores is $84$, ...
1
vote
3answers
344 views

Possibility that two students answer the same on a 25 question multiple choice test

I am trying to get some approximation of the possibility that two students would answer $25$ questions in a row exactly the same. There are 4 possible responses for each question. I calculate the ...
1
vote
3answers
87 views

Difference between these two standard deviation formulas?

Today I started reading statistics and I came across these two S.D formulas: $$\sqrt{\frac 1 n \sum (X - \overline X)^2} \textrm{ and } \sqrt{\frac 1 {n-1}\sum (X - \overline X)^2}$$ What is the ...