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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21 views

What is the difference between the natures of finding average value using secant slope and integral?

To my knowledge, there are two ways of finding average (what average I am not too sure, forgot what my teacher said. But I think it has something to do with the mean value theorem) Say you have a ...
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44 views

Propagation of Uncertainties [closed]

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...
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80 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 ...
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52 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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117 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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46 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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81 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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63 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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1k 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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47 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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65 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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122 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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240 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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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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2k 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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62 views

Calculating the average speed of a trip when given 3 different speeds for 3 percentages of distances.

The question: In a trip, $10$% of the way, Lucy drives uphill at an average speed of $56$mph; $10$% of the distance is downhill where she can manage an average speed of $72$mph. On flat ground, Lucy ...
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17 views

Using double integration to compute an average yields a different result than computing it without integration

I'm self-learning multivariable calculus and am using double integration to compute the average value of $f(x,y)$ over some region. I'm trying to solve the following simple problem using two different ...
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26 views

Average case of element comparisons when searching for an element x with a specific probability

I just had a midterm, and unfortunately our professor has stated that he will neither discuss nor post any solutions to the midterm, so I'm posting a question that was on it here in hopes that someone ...
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40 views

For all real a, b, order the averages.

I'm taking a proofs class and the textbook says to do this problem: For all real $ a, b > 0 $, show $ \dfrac{2ab}{a + b} \leq \sqrt{ab} \leq \dfrac{a + b}{2} \leq \sqrt{\dfrac{a^2 + b^2}{2}} $ ...
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288 views

Is the point of a shape with the greatest average ray length also the “centroid”?

By a shape I mean one with a enclosed area. One example can be with $x^2+y^2+\sin{4x}+\sin{4y}=4$. I am dealing with implicit relations on a 2-d plane. By the "ray length" I mean the length of the ...
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92 views

Finding average of denominator knowing average of numerator and average of fraction [closed]

Good day to you all. I have a little problem I have been banging my head on for a while. I have come to think that it is impossible, but I hope you can save me. I have a fraction, $ ...
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39 views

Is it possible to find the mean of more than two points on a number line?

I know you can find the mean of two points on a number line, just as you can find the mean of two numbers. However, I would like to know, is it possible to find the mean of THREE or more points on a ...
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25 views

Limit of sequence that depends on another.

I'm a little confused about the following problem: The sequence $a_n$ tends to $a$. Show that $b_n:=\frac{1}{n+1}(a_0+a_1+\cdots+a_n)$ tends to $a$ aswell. It looks like $b_n$ is simply the average ...
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52 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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43 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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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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38 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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148 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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662 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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537 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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2k 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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59 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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468 views

Calculate the average sales per day in 2010.

In 2005, Company K was 730 000 units of the car market. Total sales is 50% of the total cars sold in 2010. Calculate the average sales per day in 2010. Calculation: Total sales in 2010 = $50\% ...
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2k 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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211 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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193 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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292 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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22 views

Looking for an equation that reflects the majority of a collection

I'm working on a computer program, part of which involves sifting through large collections of numbers (by large, I mean 16 million+ numbers). I expect these collections to almost entirely be composed ...
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21 views

Calculate average time of person in system when ins and outs are roughly equal

I have a system that has people going through a sensor for in, a sensor for out. I'm measuring ins and outs through the day, ...
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57 views

How can I curve a test grade knowing only the average and the highest score?

I am trying to get a raw score for my test grade, but I don't know anything about the distribution of test grades; all the information I have is the average and the highest score (and of course my own ...
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50 views

Attaining the expected value over iterations

Is my implementation of the expected value correct? I conclude that the average number of iteration of this algorithm will be 1/3, but seems completely wrong. Rand() outputs either 0 or 1 (uniform) ...
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32 views

Given the lengths of two sides of a triangle, is it possible to obtain (sharp) bounds for the average length of the sides of the triangle?

The title says it all. Given the lengths of two sides of a triangle, is it possible to obtain (sharp) bounds for the average length of the sides of the triangle? Let the lengths of two sides of ...
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1answer
26 views

What is the proper notation for the “average of the last N elements of a sequence”?

I use sliding window average in my calculations: average for the last N elements and average for the N elements before that. What would be the correct mathematical notation to describe this?
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20 views

Average distance to the closest neighbor

Suppose that 3-dimensional space contains countably infinite number of randomly positioned particles (points), on average $1$ particle per a unit of volume. Their distribution is homogeneous and ...
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15 views

Difference between Means is the Mean of the Differences

Suppose you have a sequence $a_{1}, \dots, a_{n}$ and another sequence $b_{1}, \dots, b_{m}$, where $n$ and $m$ may differ. I want to know whether the difference between the arithmetic means of these ...
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36 views

Averages of Power Sets

I've been studying power sets and thought this was interesting. $\frac{x+y+\frac{x+y}{2}}{3} = \frac{x+y}{2}$ This is if we have a set of 2 elements, x and y, and we get it's powerset, find the ...
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47 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
78 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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12 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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251 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 ...