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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1answer
52 views

Average question GRE

The average daily temperature from 9th to 16th January(both inclusive) was 38.6 C and that from the 10th to 17th January(inclusive) was 39.2 C. what was the temperature on 17th January? I am able ...
2
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1answer
30 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
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1answer
19 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
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1answer
37 views

Derivation of Running(Online) Variance's formula

I need to know the dimostration of Running Variance's formula: $$ \sigma_n^2 =\frac{(n-1)\sigma_{n-1}^{2}+(x_n-\overline{x}_{n-1})\cdot(x_n-\overline{x}_{n})}{n} $$
2
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1answer
42 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
67 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
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1answer
165 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
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1answer
83 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
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1answer
307 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
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1answer
171 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, ... ...
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1answer
4k 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
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1answer
136 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
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1answer
247 views

Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
2
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1answer
311 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
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1answer
117 views

How are Tr(AB) results restricted?

In quantum mechanics one postulates that for each state $i$ there is a matrix $A_i$ and for each measureable dynamical variable $j$ (velocity etc.) there is a matrix $B_j$. Both are Hermitian matrices ...
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0answers
21 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
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2answers
42 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
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0answers
60 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
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1answer
73 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. ...
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1answer
56 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
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0answers
39 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
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0answers
71 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 ...
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2answers
55 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
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1answer
125 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
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3answers
5k views

Standard deviation of the weighted mean [duplicate]

How do you find the standard deviation of the weighted mean? The weighted mean is defined: $\bar{x}_w = \frac{\sum{wx}}{\sum{w}}$ The weighted standard deviation (since it is not specified, I take ...
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0answers
28 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
257 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 ...
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0answers
224 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
448 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
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2answers
40 views

Is it possible for it to be impossible to get to work on time? [closed]

This might sound like a homework thing but it's not - it's actually a thought I had as I sat in a traffic jam this morning on the way to work... The context of the problem is simply driving from your ...
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5answers
152 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 ...
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2answers
75 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.
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1answer
171 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 ...
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2answers
113 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 $$ ...
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2answers
34 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 ...
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1answer
2k 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, ...
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1answer
42 views

What is the name of this “generalized sum”?

I'm looking for the name of this quite basic function: $X=\sqrt[\alpha]{\sum_i{x_i^\alpha}}$ ($\alpha\in\mathbb R$) It's a kind of "generalized sum": $\alpha=1$ : $X=\sum_i{x_i}$ $\alpha\to\infty$ ...
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4answers
2k views

Fastest Method to solve this average problem

average of A and B is 71; of B and C is 76; of A and C is 79. How to find the average of A,B,C. I know the way of solving this problem using equations.But it takes time.So wanted to know if any other ...
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2answers
5k views

Is the average of the averages equal to the average of all the numbers originally averaged?

I am tempted to say yes because of the following pseudo-proof (I say pseudo-proof because I am not convinced): $$ \frac{\frac{w+x}{2}+\frac{y+z}{2}}{2}=\frac{w+x}{4}+\frac{y+z}{4}=\frac{w+x+y+z}{4} ...
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1answer
3k views

Proving correlation coefficient = 1 or -1 given X and Y=a + bX

Given $X$ and $Y = a+bX$, I have to prove that: If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$. I've gotten to the point where I have: $$ \rho = \frac{b \cdot \sigma_x }{ ...
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2answers
34 views

Calculate the average as numbers arrive

So, suppose you have to calculate the average of a set of numbers, but you don't know the whole set yet. Someone is providing you one number after the other and you cannot use more than the current ...
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2answers
240 views

what is the difference between average and expected value?

I have been going through the definition of expected value in Wikipedia (http://en.wikipedia.org/wiki/Expected_value) beneath all that jargon it seems that the expected value of a distribution is the ...
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3answers
48 views

Covariance Issue with a joint distribution

Here is the problem: Let $X$ and $Y$ be continuous random variables with joint density function: $$f(x,y) = \frac{8}{3}xy\text{ for }0 \le x \le 1\text{ and }x \le y \le 2x $$ I'm trying to find ...
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1answer
68 views

Prove inequality of generalized means

Consider the generalized (power) mean of positive numbers $a_1, \dotsc, a_n$ $$M_p(a_1, \dotsc, a_n)=\left(\frac{a_1^p + \dotsb + a_n^p}{n}\right)^{1/p}\qquad p\in \mathbb{R}$$ where for $p=0$ we use ...
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2answers
390 views

Working out a percentage of from values

Using the following numbers as an example: 293.21 478.93 485.44 544.78 569.48 593.82 I know how work out the average (mean) value: ...
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1answer
93 views

Help with my math problem, 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 ...
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3answers
43 views

Average value of recurrent function.

Given a function f(x) = a*f(x-1) where a is a number between 0 and 1, what is the average value of ...
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2answers
58 views

Problem Solving using Algebra

If Peter is $7$ years older than Sharon and John is twice as old as Peter, work out how old Peter is if the average of their ages is $19$. Thanks! :)
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1answer
89 views

Why 1 / (average of series) $\ne$ average (1 / series)

I have series of two stocks prices. Let's say that stock 1 has prices: $A_1$, $A_2$, $A_3$, $A_4$, ..., $A_i$ (where $i$ is time) And stock 2 has prices: $B_1$, $B_2$, $B_3$, $B_4$, ..., $B_i$ ...
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2answers
198 views

Average limit superior [duplicate]

Let $\mathcal{l}_\mathbb{R}^\infty$ be the space of bounded sequences in $\mathbb{R}$. We define a map $p: \mathcal{l}_\mathbb{R}^\infty\to\mathbb{R}$ by $$p(\underline x)=\limsup_{n\to\infty} ...