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.

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46 views

How do the Averages Work?

I am trying to figure out the average items sold per customer for the year 2019 I have multiple customers per day, who each have a random number of items. Sometimes a customer makes more than one ...
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How to do complex weighted average math [duplicate]

Hello I tried to ask this question but it was closed. I didn't understand why nether where should I put this question ? I still believe it is a math problem but please advise if there any other place ...
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Claims on insurance average? [closed]

I can't calculate this example: can somebody please help me out? For an insurance, it is important to evaluate how many claims per insured person occur. Experience has shown that in recent years 80% ...
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Finding average from uniformly distributed values

Let's say, I am sending network packets at the rate of 450 packets per second. The size of these packets is uniformly distributed between 100 to 500 bytes. I want to know what's the average packet ...
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Is this weighted average smaller than the corresponding arithmetic average?

Is it true that the following weighted-average is smaller than the respective arithmetic average $$ \sum_{n=1}^{N}\left(\frac{b_{n}}{\sum_{m=1}^{N}b_{m}}\right)\frac{a_{n}}{b_{n}}\overset{?}{\le}\frac{...
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Fidning average time it takes to finish a job

$30\%$ finish their job in $122\mathrm s$, $30\%$ finish their job in $68\mathrm s$, and $40\%$ finish their job in $190\mathrm s$. What is the average time it takes for a person to finish their job? ...
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Work capacity of a group

Looking for help on how to get the work capacity of two groups and if my calculations and process are valid. I have two groups (A and B) who process calls. It takes both groups an average of 4 ...
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How many kinds of average are there?

I have learned that the mean, median and mode are three kinds of average. Are there other kinds of average or are there just these three ?
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Can an average of an overall set be equal to the average of a subset?

I read in a publication that the average salary for lawyers in America is $\bar x=\$163,595$. Of these salaries, the average for men is $\bar x_m=\$183,687$, and for women, it is $\bar x_w=\$163,595$. ...
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Average Distance for Unit Ball

Let $B$ be a unit ball in $\mathbb{R}^3$. Find the average distance from points in $B$ to the origin. My progress: If I am not mistaken, this problem should be solved by triple integrals and the ...
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Can I calculate how good I am if I know my score and the average score?

If I know the average score of all participants (46/100) and I know that there are ~1500 participants, and my score is 90/100, can I somehow calculate what percentage of people I’m in? (Eg top 10% of ...
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Time averages for a 2-dimensional harmonic oscillator

I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it. Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\...
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Mean of fractions or fraction of means? When to use mediant and when to use mean? [duplicate]

When would we use the mediant? Clarifying the problem: I was working on some numbers. De data had duration of a job, the number of steps to complete a job and the starting date of a job. All rows had ...
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Analyzing a definition of average which uses a variation of the Lebesgue integral and measure [closed]

Edit: Why was my post downvoted. Please explain how I can improve my post. Second Edit: I changed my Post Introduction Consider $f:A\to[a,b]$ where $A\subseteq[a,b]$ and $S\subseteq A$. I want to ...
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compute cumulative average

I have below table which i compute the average in the end of the month. ...
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Find median of a combination of tables.

Values in List $P$ are distinct from values in List $Q$. List $R$ consists of all the values in list $P$ and all the values in list $Q$. Find the median of list $R$. My logic: Here the total number ...
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Interpreting the Weighted Pinball Loss

I am participating in a Kaggle competition and came across the Weighted Pinball Loss function for the first time and I don't quite understand it. Here is a screen shot of the definition provided by ...
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How do I calculate average? and What does per 100 word mean?

- 295 letter(s) - 70 word(s) - 3 sentence(s) How do I calculate ? Average number of letters per 100 words. Average number of sentences per 100 words. I know ...
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A variant of Jensen inequality when the function is not everywhere convex

Let $F:(0,\infty) \to [0,\infty)$ be a $C^1$ function satisfying $F(1)=0$, which is strictly increasing on $[1,\infty)$, and strictly decreasing on $(0,1]$. Suppose also that $F$ is convex on $(0,1]$...
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How to average directional data?

Assume that I have a collection of vectors $v_i,i=1,...,N$ in some multi-dimensional space $v_i \in \mathbb{R}^d$. For simplicity, we can assume that the norm of all vectors is unity ($||v_i||=1 \...
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How do you find the centre of gravity using moments?

I'm just working through this example (Example 2), using moments and resolving forces to find the centre of gravity of three particles. I understand resolving the forces and finding $\bar{x}$, but I ...
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Unknown Math symbol (Calligraphic I in Statistics)

I came across a symbol I cannot figure out the meaning of. I found it in the LaTeX chart as a calligraphic I. This is the symbol in an equation for a bin weight in an RBF kernel circular local ...
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Payout amount dependent upon value for each person in population

I am a software developer tasked with solving a problem programmatically, but I'm limited in what I remember about statistics and am not sure how to properly word my question to search for the answer. ...
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Ensemble Average of Squared Function - Paper passage

On the paper: "Analysis of Subthreshold Current Reset Noise in Image Sensors" which can be publicly found here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4883354/ the author is using a method to ...
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Show that if $\lVert a_{pn}\rVert>0$ for primes $p$, then $\lVert a_n \rVert\geq0$

If we define $$\lVert a_n\rVert = \lim_{N\to\infty}\frac{1}{N}\sum_{k=0}^{N-1}a_k$$ To be the mean of a sequence, and we let $a_n$ be a bounded sequence of integers where not only does $\lVert a_n\...
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How do prove this integral, defined on a countable set with infinite limit points, converges to zero?

Consider a continuous $f:A\to[0,1]$ where $A\subseteq[0,1]$. Edit: I did not use @Mathworker21's answer because I assumed it would not give the result I am looking for. Now I change my mind. Here is ...
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What is the average value of x? [closed]

I came up with this math script x=0; x+=Ran#ⁿ, n=0…1000000000 Ran# is a random number generator that returns a uniform random real number from 0 (inclusive) to 1 (exclusive) ⁿ is to take the random ...
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Measuring average time

I have a dataset of times (time to execute a task) and I'm now interested in calculating the average time. I might just be mixing stuff up and doing it more complicated than it is but.. The time's ...
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weighted average with strictly positive weights

This is a terminological question: say $y$ is a weighted average of $x_1, \dots, x_n$ if $y=\sum_i w_i x_i$ for some set of weights $0\leq w_1, \dots, w_n\leq 1$ with $\sum_i w_i=1$. I am curious if ...
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The Jensen gap $\mathbb{E}[|\overline X|] - |\mu|$

Let $ X_1, X_2, \dots, X_n $ be a sequence of i.i.d. random variables with finite mean $ \mu $ and variance $ \sigma^2 $. Let $ \overline X = \frac{1}{n}\sum_{i=1}^n X_i $ denote the sample average. I ...
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Dividing largest eigenvalue of distance matrix by number of coordinates

I am working with a set of vectors and I constructed a matrix that shows all pairwise Euclidean distances between them. Thus this distance matrix has zeros along the main diagonal. Part of the project ...
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Assigning positive weight for data set having both positive and negative numbers

I have a data set containing both positive and negative numbers. Say, for example the following $10$ values: 11, 45, 68, -18, 29, 22, -8, -12, 54, 33 I have to ...
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Understanding Moving Average Models

Can someone explain why we use past errors to predict future data values in Moving Average models? It just doesn't make sense why we use past errors to make predictions. Using past values, as in $\...
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Integral as an average and normalisation

There are some mathematical aspects I do not really understand from my macroeconomics course. For labour $N_t$ and capital $K_t$ following equations are given: $$N_t=\int_{0}^1 N_{jt} dj=1 \qquad (1)...
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How do we define an “intuitive” average on this function?

Say we have $P:A\to[0,1]$ where $A\subseteq \mathbb{R}$ $$P(x)=\begin{cases} x^2+5 & x\in\left\{\frac{1}{a}:a\in\mathbb{N}\right\}\cup\left\{\frac{1}{b^{\sqrt{2}}+0.1}+\frac{1}{5}:b\in\mathbb{Z}\...
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calculating expected hours for widget production over time

I created some R code below to clarify my question a bit more. Basically, I have widget that are produced (identified by ids). The require a certain amount of hours per month. So I have measurements ...
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How do we create a better definition (for my definition of average) which is easier to compute and gives exact values?

This not the same as "Coming up with a rigorous definition for a Riemann-like sum which is easier to compute? ". Here I'm assuming my Riemann-like sum is clear enough to understand. If not, try and ...
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Find the average of $P$ defined on the Fat Cantor set

Suppose we have $P:A\to[0,1]$, where $A$ is the fat cantor set denoted as $C$. We produce $C$ by removing $1/4$ of $[0,1]$ around mid-point $1/2$ $$C_{1}=[0,3/8]\cup [5/8,1]$$ $$C_{1,1}=[0,3/8] \ \ ...
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Find the average of a function defined on a Fat Cantor Set

Suppose we have $P:A\to[0,1]$, where $A$ is the fat cantor set denoted as $C$. We produce $C$ by removing $1/4$ of $[0,1]$ around mid-point $1/2$ $$C_{1}=[0,3/8]\cup [5/8,1]$$ $$C_{1,1}=[0,3/8] \ \ ...
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How can I get a real average from many measurements?

I am measuring fuel level from a car. I am getting too many different values. for example: the real value on the car's board is 50%. when I measure 10 successive values: 51% | 50% | 49% | 56% | 51%...
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Time Average: When Does this Limit Exist?

The background of this question is Quantum Optics for me, or more specifically classical coherence functions. Nevertheless, I believe this function to be applicable to a wide range of topic where time ...
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119 views

Average of function defined on cantor set

Suppose we have $P: A\cap[0,1]\to\mathbb{R}$, where $A$ is the Cantor set. I want to define and find the average of $P$ to give a result between the infimum and supremum of $P$'s range. Obviously we ...
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Cross correlation of signal with its average vs cross correlation between two signals

In signal processing we often use cross-correlation to determine a phase difference between two signals. Now usually we calculate the phase difference $\tau_A$ between the two signals $f$ and $g$ by ...
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1answer
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Pick a New Average And Find the Number of Units to Add [closed]

I'm looking for a formula to find how many units I have to add to an existing average in order to get to a new average that I set before. Example: I have an average of scores 82 that includes 17 ...
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Proportion of above-average values in a sequence of sums

Suppose $X_1, \ldots, X_n \in \mathbb R$ and $Y_1, \ldots, Y_m \in \mathbb R$. Let $\mu_X = \frac{1}{n} \sum_{i = 1}^n X_i$ and $\mu_Y = \frac{1}{m} \sum_{j = 1}^m Y_j$ be the averages of the $X_i$ ...
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Maximize weights in a weighted average using Lagrange multipliers

For values $\mathbf{a}=(a_1, a_2, ..., a_N)$ with corresponding weights $\mathbf{w}=(w_1, w_2, ..., w_N)$ (assume $\sum_{i=1}^{N} w_i = 1$ and $0 \le w_j \le 1$ for $j \in {\{1,2,...,N\}}$), the ...
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Mean distance of of points in disc to the origin

Is it simply ( $\sin \alpha =\frac{R}{d}$) $$ \dfrac{\int_\alpha^{+\alpha}\int^{d+R}_{d-R} r^2 dr d\theta}{\pi R^2}? $$ We have a definitions of second moments of area about $x,y,z\,$ axes. What ...
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Could we define an average that satisfied all the conditions below? If so, how?

I posted this question on Math Overflow if you wish to answer there. Consider $P:A\to\mathbb{R}$, where $A$ is a subset of $\mathbb{R}$. I want the average of $P$ to ALWAYS be between the infimum ...
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1answer
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Average of Block Vectors

Let $x$ be a block vector with two vector elements, $x=(a,b)$ where $a$ and $b$ are vectors of size $n$ and $m$, respectively. Express $avg(x)$ in terms of $avg(a)$, $avg(b)$, $m$, and $n$.
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Average Distance Between Two Points on a Line

I know this question has been answered many times, but I wanted to verify another method to solve this that I couldn’t find elsewhere. So I did the following: I fixed a point P distant $d$ from one ...

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