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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177 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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1answer
57 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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1answer
3k views

Use calculus to calculate the slope of a moving average line

I recently read a paper where it was stated that calculus was used to calculate the slope of a moving average line at a given point. Given that there is no real formula to differentiate with a moving ...
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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 }{ \sqrt{\...
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23 views

Reporting numbers that vary

I'm timing how long various parts of a computer program takes to run, with the intent of including this in a research paper. There are fluctuations in the timing based on the usual things inside a ...
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1answer
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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1answer
50 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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56 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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194 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
58 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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89 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
67 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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3answers
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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2answers
67 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
129 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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241 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} \frac{1}...
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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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1answer
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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4k 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
63 views

2 trams are coming every 5 and 10 minutes. On average, how long do I have to wait for any tram to come?

I want to follow the approach from Christian Blatter here 3 trams are coming every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come? using "the assumption that the ...
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1answer
35 views

Which is the proper way to calculate average speed.

Let's say we have a graph, a distance-time graph, and there are couple points on the graph. The points are connected to each other with different slopes, so with different speeds between the points. ...
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114 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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18 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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1answer
28 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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1answer
45 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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5answers
291 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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2answers
43 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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2answers
26 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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1answer
54 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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1answer
85 views

Average of elements in a subset of $\{1,2,3,..,n\}$ is greater than $\frac{n+1}{2}$ [closed]

Consider two integers $n \ge m \ge 4$ and $A=\{a_1,a_2,...,a_m\}$ a subset of the set $\{1,2,3,...,n\}$ with the property that $$\forall a,b \in A \text{ with } a \neq b, \text{ if } a+b \le n, \text{ ...
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3answers
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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2answers
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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1answer
180 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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1answer
699 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
636 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
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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485 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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1answer
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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1answer
221 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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200 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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306 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
24 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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1answer
26 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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1answer
63 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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1answer
56 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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1answer
35 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 ...