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
116 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 ...
2
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0answers
47 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
35 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
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1answer
52 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
69 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
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2answers
53 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
106 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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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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3answers
4k 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
25 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
166 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
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0answers
209 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
418 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 ...
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5answers
139 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
152 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
66 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
30 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
1k 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
37 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
1k 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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1answer
2k 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
65 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
37 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
20 views

How to calculate new mean if population is unknown?

I have three values Mean (population mean, not from sample) $\bar{x} = 3$ Number of elements in population (number of values in original set) $n = 15$ A new value $x_{(n+1)} = 7$ What is ...
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1answer
44 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
116 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
58 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
41 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
53 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
76 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
172 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} ...
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2answers
329 views

from weighted average to single values

think about when you're computing a weighted average: you do something like W = sum(amount*weight) / sum(weight) Now I need to find every amount (amount0, amount1.....) starting from knowing the ...
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2answers
53 views

Constructing an average equation - Standardized Test

A question in the standardized test is: The average of $n$ numbers is $a$. If $x$ is subtracted from each number the average will be a) $(ax)/n\quad$ b) $(an)/x\quad$ c) $an-x\quad$ d) ...
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2answers
4k 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
798 views

Calculating the mean from an exponential distribution

could someone please tell me how I can prove/confirm the information on this page? specifically the part about calculating the mean, I have my doubts about the -b. Many thanks
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3answers
3k views

Simple question regarding ratio and average

I have 2 lists of numbers (with an equal number of numbers in each). Each number is then divided by the number of which it is paired with (by index), and a ratio is received. I then want to calculate ...
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2answers
2k views

What is the standard error of the mean of an exponential distribution of the form $Ae^{Bx}$ with N measurements?

What is the standard error of the mean of an exponential distribution of the form $Ae^{Bx}$ with $N$ measurements?
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1answer
73 views

Average value of a piecewise defined function

Consider the function $f$ defined by $$ f(x) = \begin{cases} x, & 0 \leq x < 1 \\ x^2, & 1 \leq x < 2 \\ \vdots \\ x^n, & n-1 \leq x < n. \end{cases} $$ I'm trying to compute ...
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1answer
93 views

Sum of weighted squared distances is minimized by the weighted average?

Let $x_1, \ldots, x_n \in \mathbb{R}^d$ denote $n$ points in $d$-dimensional Euclidean space, and $w_1, \ldots, w_n \in \mathbb{R}_{\geq 0}$ any non-negative weights. In some paper I came across the ...
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1answer
251 views

Mean/ Expected Value of $X^4$

$\def\Var{\mathop{\rm Var}}$Can anyone help me prove that Expected Value of $X^4$ is $3\Var(X)^4$, if the Expected Value of $X$ is zero and $\Var(X)$ is the Variance of $X$? Thanks!
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1answer
63 views

Geometric Mean of an Interval

Is there any way to calculate one? If it't not clear what I mean, here's an example: Starting with an initial value, keep multiplying it by some random amount on the interval [1, 2] at regular ...
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2answers
46 views

Expected average of number of tiles empty

I have a grid of 3x4 and every tile on the grid has a corresponding chance of being empty. This chance is given. For example, consider the following grid: $$ \frac{14}{15} \frac{1}{3} \frac{8}{13} ...
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1answer
586 views

Algorithm to separate an array of numbers into “low”, “medium” and “high” ranges

this is my first post on Math-Exchange. I'm a programmer, and I work with object-oriented algorithms, but when things gets too "algebraic" I get stuck. So I thought I'd ask over here. I need to ...
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1answer
89 views

averaging time it takes to complete a project

Consider a project consisting of four activities A, B, C, and D. a) A and B, the first activities of the project, can be started simultaneously. b) C can be started only after A is completed. c) D can ...
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4answers
333 views

Finding mean of $n$ consecutive numbers using a shortcut

I am working on the following question: Let us say we have $n$ consecutive numbers labelled $x_1$ to $x_n$. I want to find the average of these. The quickest way to do this seems to be ...
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2answers
136 views

Merging/averaging percentages

This may be a very simple question, but I'm not even sure what the correct terminology is for the procedure I am trying to do so I wasn't able to find anything else here... The scenario is that I'm ...
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1answer
2k views

Weighted average vs. weighted mean

Is there a formal difference between weighted average and weighted mean? I get corrected to the latter if I type in the former in wikipedia, and then there is a lot of stuff about the name "average" ...
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1answer
204 views

Bound on deviation between arithmetic and harmonic mean?

It is well known that, if HM denotes the harmonic mean and AM the arithmetic mean, we have $$ AM(x) \ge HM(x) $$ Now I am dealing with the expression $$ \frac{1}{HM(x)} - \frac{1}{AM(x)} $$ A ...
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1answer
26 views

Sum and sum of average not matching

I'm struggling with the following problem. I have a table showing the % of a population that like (say) bananas in three locations, the population of each location, and the total population who like ...