Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [average]

Averages summarise a set of values in one way or another. Without further qualification it most commonly refers to the arithmetic mean, but other averages such as root-mean-square exist.

0
votes
0answers
25 views

Proving a theorem about the average value of a function over a specific region

Let's say transient phenomenon in a function. A transient phenomenon is defined as: "A transient event is a short-lived burst of energy in a system caused by a sudden change of state." So, for ...
0
votes
0answers
15 views

Linking two dependent equations in a moving average

I have a time discrete system where I need to perform an average of values in a total time n. However, the values are separated with different windows. The process follows like below: After each ...
0
votes
0answers
29 views

Proving a statement about the average value of a function

I'm working on a rather complicated problem. And in that problem I (for assumed) that the transient or start-up phenomenon does not influence the average value of a function. My question is, can I ...
14
votes
11answers
3k views

Why is the inverse of an average of numbers not the same as the average of the inverse of those same numbers?

I have a set of numbers (in my case: mean retention time (MRT) in the stomach (h)) of which I want to calculate the average gastric passage rate (/h). Gastric passage rate = 1/MRT. My question is why ...
1
vote
1answer
26 views

Limit of an arithmetic average series

Sorry in advance as English is not my primary language. I randomly thought of the following simple problem, and I coudn't solve it after one one hour trying. Maybe you guys can help. Let $a_1$ and $...
0
votes
0answers
16 views

Sliding weight equation used for temperature averaging

I've looked for previous related questions with no luck, so I apologize if this has already been answered. I may not be phrasing it correctly! I am trying to determine a weighted average that is ...
0
votes
3answers
31 views

Calculate the winning probability when using two dice with a different number of sides

I have two players with one die. The first player throws a die between 1 and 125. The second player throws a die between 1 and 350. The winner is the person who gets the higher roll. How do I ...
0
votes
0answers
15 views

Random walk with accumulation of penalties

Let a random walf with a certain stopping time $T$. Say that step $i$ costs $i$. If we can compute the average value of $T$, what is the correct (non biaised) way to compute the average cost? Le $E(...
5
votes
2answers
431 views

Find a number having minimum sum of distances between a set of numbers

Lets say we have a set of numbers $\{ 5, 7, 1, 2, 5, 100 \}$. I want to find a number $x$ such that the sum of distances of every number from the set to $x$ is minimal. My first thought was that $x$ ...
0
votes
1answer
29 views

Average calculation

I know it will be a stupid question for somebody but I need to understand. Below the matrix: $$ \left[ \begin{array}{cc|c} 55&0&0\\ 55&0&0\\ 15&8&53\\ 15&4&27\...
1
vote
1answer
11 views

Calculate average/probability of an action happening in a shrinking pool

I'm not sure how to title this actually, so I'll try to explain it better. Let's say I have a bag of 50 items. In there is one particular item that I want. Obviously, the probably of getting that ...
1
vote
2answers
59 views

Prove the following logarithm inequality.

If $x, y \in (0, 1)$ and $x+y=1$, prove that $x\log(x)+y\log(y) \geq \frac {\log(x)+\log(y)} {2}$. I transformed the LHS to $\log(x^xy^y)$ and the RHS to $\log(\sqrt{xy})$, from where we get that $...
3
votes
1answer
117 views

Darboux continuity of the function $f(x) = \limsup_{n \to \infty} \frac{(x_{1}+…+x_{n})^{2}}{n^{2}}$

Let $f : [0,1] \to [0,1]$ be a function that assigns to each $x \in [0,1]$ the following value: $$ x = 0.x_{1}x_{2}x_{3} \ \ ... \hspace{0.3cm} \text{be the binary expansion of }x $$ define $$ f(x): ...
0
votes
0answers
14 views

Best Average to Represent Quantitative Data?

For a final assignment, my two group members and I have created a biased survey called Should Public Schools Implement a Uniform Policy? We have about 2-3 ...
1
vote
1answer
24 views

significant figures in averaging samples

I can't seem to find anything about this but I thought that for every 10 samples (of the same thing) that you averaged together you gained 1 significant figure. You'd maybe need 100 samples to gain 2 ...
8
votes
4answers
252 views

If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?

I was thinking of periodic functions, and in particular the following type of condition: If a function $f:\mathbb{R}\to\mathbb{R}$ always "tends to its average", then it should be periodic. To ...
0
votes
0answers
32 views

Calculate average wind velocity

I've got an anemometer to measure wind speed. Its ratio is $50Hz = 15.5m/s$, so my Arduino counts pulses in 3100ms, which should give a count of $100 = 10m/s$. I can display this on a dashboard on ...
4
votes
1answer
79 views

Generalized AM-GM Inequality

I was discussing means with my friend, and I tried to illustrate the concept of geometric mean using the following idea: Suppose we have two positive quantities $x,y>0$. The simplest geometric ...
3
votes
2answers
66 views

Proving that a solution to a differential equation is monotonic

The answer that ws given on a previous question of mine, stated that the solution to this DE: $$x(t)\cdot r+x'(t)\cdot l+a\cdot\ln\left(1+\frac{x(t)}{b}\right)=0\space\Longleftrightarrow\space x(t)=\...
5
votes
1answer
66 views

Average of a function that comes out of a complicated DE

I've to find (the average of a function over a particular interval, where $t_1>0$, $t_2>0$ and $t_2>t_1$): $$\frac{1}{t_2-t_1}\int_{t_1}^{t_2}x(t)dt\tag1$$ Where $x(t)$ is the solution to ...
1
vote
0answers
31 views

A minimizing property of the Sphere?

From the wiki “Sphere” entry: “The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface ...
0
votes
1answer
33 views

Can I average percentage differences?

I know I can't average percentages, but can I average percentage differences. For example, I've calculated the Mean Absolute Error (MAE) of two forecasts (same sample sizes) and the percentage ...
0
votes
0answers
35 views

Proving $\mathbb{E}\max\{\xi^2,\eta^2\}\leq 1 + \sqrt{1-\rho^2}$ [duplicate]

Let $\xi$ and $\eta$ be random variables and $\mathbb{E}\xi=\mathbb{E}\eta=0$ also $\mathbb{D}\xi=\mathbb{D}\eta=1$. Here $\rho=\rho(\xi,\eta)$ is a correlation coefficient. Need to show $$\mathbb{E}\...
0
votes
1answer
31 views

Which mean to use to find the average of measurements given in the form of “per period”

Let's say I made several measurements on my gas consumption. $2$ m$^3$ per day $1$ m$^3$ per day $1.5$ m$^3$ per day $2$ m$^3$ per day What is the average daily consumption of gas? I can take ...
0
votes
0answers
29 views

Proving $\inf_{a \in \mathbb{R}} \mathbb{E}|\xi -a| = \mathbb{E}|\xi - m\xi|$ [duplicate]

Let $\xi$ be a random variable form $(\Omega, \mathcal{F}, \mathbb{P})$. Than let $m\xi$ be a median of random variable $\xi$. I need to prove $$\inf_{a \in \mathbb{R}} \mathbb{E}|\xi -a| = \mathbb{E}|...
0
votes
1answer
44 views

Balls and boxes. Average

We have $r$ balls and $n$ boxes. We took all balls to boxes randomly. Find the average of empty boxes. So I think there are two ways. When $r<n$ and $r\geq n$. When $r<n$ thank can be $1,2,3,.....
1
vote
1answer
35 views

What's the average life expectancy if only dying from accidents?

So, I curious and trying to determine what sort life expectancy a human being would have if they were immortal (as in, no more senescence (aging)). Accidental deaths only. I've googled around and ...
0
votes
0answers
9 views

Trouble with understanding notation regarding successive terms in the expansion

Another symmetric example(of moving average) is provided by the case where the ${a_r}$ are successive terms in the expansion of $(\frac{1}{2} + \frac{1}{2}s)^{2q}$, where $s$ denotes a dummy ...
3
votes
2answers
315 views

Weights of simple moving average are not adding up to one

This is the definition of linear filter from a book I am reading: A second procedure for dealing with a trend is to use a linear filter, which converts one time series, $\{x_t\}$, into another, $\{...
1
vote
2answers
35 views

How to calculate average on set of data points where recent data has more weight

Take for example this dataset: [1,1,1,1,1,1,1,1,1,200,1,1,1,1,....,1] I want to calculate a running average on this with a certain window size for avg, let's say ...
-1
votes
1answer
33 views

Simple question about averages

I have got feedback from a survey where the range is 1-10, where: ...
107
votes
15answers
19k views

The math behind Warren Buffet's famous rule – never lose money

This is a question about a mathematical concept, but I think I will be able to ask the question better with a little bit of background first. Warren Buffet famously provided 2 rules to investing: ...
1
vote
1answer
26 views

When does it make sense to find a point between two points?

I have this need to be able to express when a point is "between" two other points. One great example is the binary average operation $Avg:R \times R \rightarrow R$ that takes two real numbers and ...
1
vote
1answer
23 views

Which average would make the most sense (mean, mode, median)?

I have musical data, for tuning information for notes of an instrument. For each note played, I have the cents away from in tune (-50.0 - 50.0). I'd like to display the average each note was out of ...
0
votes
1answer
11 views

Weight the probability of a prediction based on historical accuracy

I have six predictions from six different sources. Each prediction has a percent probability that the prediction will happen, as well as a historical accuracy percentage. Here's a table of my problem:...
1
vote
2answers
36 views

Point $x \in \mathbb{R}^n$ that minimizes sum of distance squares $\sum_{\mathcal{l}=1}^{k} \Vert x-a^{\mathcal{(l)}} \Vert _2^2$

Let $a^{(1)},...,a^{(k)} \in \mathbb{R}^n$. How can one find the point $x \in \mathbb{R}^n$, which minimizes the sum of distance squares $\sum_{\mathcal{l}=1}^{k} \Vert x-a^{\mathcal{(l)}} \Vert _2^2$...
0
votes
2answers
64 views

Expected value of sum of N sines with random phase differences

This is a follow-up to this question. It discusses the amplitude of a sum of $N$ functions of the form $a\sin(kx+c)$ $\sum_{i=1}^{N} a\sin(kx+c_i)$ with $a$ and $k$ constant and $c_i$ random numbers ...
0
votes
0answers
18 views

What is the best formula for calculating average based on count?

I would like to calculate an average of the series based on the count. Say, for example, Series 1 (10 values): 5, 1, 2, 3, 4, 5, 4, 1, 2, 3 Average: 30 / 10 = 3 Series 2 (2 values): 3, 4 ...
0
votes
2answers
36 views

How to find the average value/sum of combinations with repetitions

Let's say I have a set $\{1, 2, ...x\}$ and pick every distinct combination of length 3 (including repeated numbers) and create a new set by adding values equal to the product of the elements in each ...
0
votes
0answers
12 views

Statistics: Higher confidence, higher weight

So we have an experiment going on where a group of colleagues evaluate each other's skill levels, ranging from 1 to 5. We have $n$ colleagues, so in the end we should get $n^2$ evaluations. However, ...
0
votes
0answers
14 views

Geometric average less or equal to arithmetic one [duplicate]

Let $\ $ ${y_1\cdot...\cdot y_n} \in \mathbb{R}$ $\ $ be positive $\quad$ Prove: $\sqrt[n]{y_1\cdot...\cdot y_n}$ $\le$ $\frac{y_1+...+y_n}{n}$ I have tried to find this by searching keywords like ...
2
votes
0answers
46 views

Limit of a recursive sequences involving the AM, GM, and HM (arithmetic-geometric-harmonic mean)

Let $x,y,z$ be positive real numbers. And let $\text{AM}$, $\text{GM}$, $\text{HM}$ respectively be the arithmetic mean, geometric mean, and harmonic mean. Define $$a_n=\text{AM}(a_{n-1},g_{n-1},h_{...
0
votes
2answers
25 views

Confusing question on finding mean from frequency tables.

My attempt: The missing frequency = 6 (from 50 games which represents total frequency) Total number of tickets won by Adan = 203 Mean number of tickets won per game = $\frac{203}{50}=4.06$ From ...
0
votes
0answers
28 views

Averages…Numbers in a list

I have provided many submissions and all of them have been wrong. Not sure what else I can do so I am asking here. Give a formula that computes the number of operations required to find the average ...
4
votes
1answer
126 views

What is the maximum value of $n$ with average value must be an integer?

Let $M$ be a positive integer greater than $1$. All integers from $1$ to $M$ were written on a board. Each time we erase a positive integer on the board in a way that the average value of all ...
0
votes
2answers
43 views

Is There a Better Algorithm for Finding the Minimum Potential Set of Integers that Could Comprise a Given Mean?

I'm trying to find the inverse of the mean, or in other words find the set of positive integers between an inclusive range that equals the mean, when divided by the number of integers identified. ...
0
votes
0answers
25 views

The 'Circular Average' of a collection of points on the Unit Circle

When dealing with quantities modulo $2\pi$, one naturally wants to know if the concept of 'arithmetic mean' can be extended. One way of doing this would be to project each 'angle' to the unit circle ...
1
vote
0answers
35 views

Average percentage overlap between two/more datasets

I am analyzing different schemes of mutual funds. Each scheme has many funds in its portfolio. I wanted to analyse the overlap (of funds) between these schemes. I can find the overlapping of scheme1 ...
2
votes
1answer
40 views

If $\lim_{n \rightarrow \infty }s_n = s$, is it true that $\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{k=1}^n s_k =s $ as well? [duplicate]

If $\{s_n\}$ is a sequence of positive real numbers such that $\lim_{n \rightarrow \infty }s_n = s$, is it true that $\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{k=1}^n s_k =s $ as well?
0
votes
0answers
14 views

Growth rates of averages does not make sense. Why?

Been struggling with this and can't explain it. Picture Link to google sheets For a school project I need to compute the revenue per store and the implied growth rate of the revenue per store. What ...