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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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
205 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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191 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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39 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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63 views

Mean age among employees in a company.

In a company there are 32 men and 59 women. Male mean age is 48.5 and female 39.2. One of the women (47 years old) ended working at the company and was replaced with a 23 year old man. Calculate the ...
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3answers
2k 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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1answer
44 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
3k 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
7k 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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37 views

Infinite averages

If you wanted to find the average of infinite items, what would it be? Would an estimate of the first x averaged be a good estimate? Or would the value be nearly zero because you are dividing by ...
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1answer
32 views

Is the nth root of a product of n terms used in place of the average anywhere?

In applied usage we typically take the average of values or terms which is done by summing them and dividing by the number of terms (for simple average): $$\sum_{i=1}^n \frac{a_i}{n}$$ It dawned on ...
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58 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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3answers
53 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
124 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
836 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
132 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
45 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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1k views

Way to aggregated percentiles

I want to have information of http response times. The average, 95 and 99 percentil. All the response times are collected in each web server, and every second is sent back to a central server that ...
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62 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
106 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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214 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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831 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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56 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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1k 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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3k 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
34 views

Could someone explain the notation of the average of quaternions equation?

The equation has some notation that is difficult to find the meaning for. It is equation (3) in the paper 'Quaternion Averaging' by F. Landis Markley, et al. on page 3 under 'The Average Quaternion'. ...
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1answer
37 views

A specific kind of Moving average

The problem is : Consider the list consisting of the first n natural numbers without zero, ie from $1$ to $n$. We define the transformation "moving average" on the list of $n$ elements by ...
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1answer
76 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 ...
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47 views

Mean of a vector

Be a set of numbers $v=(a_1, a_2, \ldots, a_n)$ I want to form the following average vector $\mu = (\frac{\sum a_i}{n}, \frac{\sum a_i}{n}, \ldots, \frac{\sum a_i}{n})$. If I do it iteratively step ...
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33 views

statistics z score

I'm curious what the phrase "on average" means. Here is an example: On average, 30% were further than ___ kilometers away when they had their accident. Is $30\%$ a $z$-score or is it a mean? ...
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1answer
87 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 ...
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2answers
7k views

What is the difference between the normal average and weighted average?

What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and also,how to get the weighted average of some ...
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1answer
381 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
352 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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1k 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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53 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
1k 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
151 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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171 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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2answers
262 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
41 views

Why this process is nonergodic?

I am studying a tutorial on stochastic processes and there's an example in it which I don't understand anything of it. First of all there is this criterion for a mean-ergodic random process: For ...
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1answer
46 views

How to summarize a big table of results? Average or Geometric mean?

I am writing a paper for a Computer Science conference and I have a big (way too big) table of results (times and some other measures) for different versions of an algorithm. I would like to summarize ...
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1answer
10 views

Grading limitless variables

I am trying to calculate the quality of a triangle. Parameters are skewness, aspect ratio, and size. Skewness ranges between 0 and 1. Aspect ratio is the ratio of longest edge to shortest edge. ...
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38 views

how do they calculate these following columns

I have these data: I am sorry the data is in Portuguese, and it is an image so I can't convert it to a table but the translate "probably" ( i am not a native speakers for Portuguese language) is: ...
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1answer
71 views

Average patients waiting time in dental office

At a Dental Office, patients come in at the rate of 20 per hour and, on average, are processed at the same rate. Patients wait in a queue till they are called up to the counter for registration. After ...
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1answer
39 views

How to find average of minimum value of two Poisson distributions?

I have two Poisson distributions with parameters $\lambda 1$ and $\lambda 2$. Now I want to find the average of minimum value of this two distributions. I mean that if I derive two random numbers ...
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2answers
78 views

Adding to an average without unknown total sum

Let's say I know the following: Let A be the average value Let T be the number of values Assuming that A = 4.3 and ...