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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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Inequalities and averages

Dikshant writes down $2 k+1$ positive integers in a list where $k$ is a positive integer. The integers are not necessarily all distinct, but there are at least three distinct integers in the list. The ...
aiman's user avatar
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What is the annualized weighted rate of return for these investments? [closed]

Example: A client has a 1-year ROR of 18% based on a 35% tax ordinary income write off, 7-year return of 5.45% on $100,000, and a 7-year return of 10% on 24,500. What is the annualized weighted rate ...
Josh Magnus's user avatar
1 vote
1 answer
24 views

Average customer value

I have a table with customer purchase data. |customer | month | Purchase amount | number of days shopped | |A | jan | 200 | 5| |A | feb | 250 | 7| | A |...
Mpl's user avatar
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1 vote
0 answers
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Weighted Average and System of Equations

Suppose I have all discrete distributions over the reals with support size N. So, I have a set of all possible weights $A=\{\alpha\in [0,1]^N:\sum_i^N\alpha_i=1\}$. Fix $\hat{b}$. Now suppose I have ...
user1328782's user avatar
0 votes
1 answer
23 views

Slopes of Translations of Convex Functions

Suppose I have a strictly increasing, continuous, convex (non-linear) function $w:\mathbb{R}\rightarrow{} \mathbb{R}$. Let $\{\alpha_i\}_1^n$ be weights that sum to 1. Fix some $x^*\in \mathbb{R}.$ ...
user1328782's user avatar
1 vote
4 answers
95 views

A possible error in a math question of 2022 Brazil's ENEM, a equivalent to US's SAT

This is a rather simple question, and it may seem like a physics question, but it actually belongs to a math test. I'll translate it into English first and then reproduce the Portuguese version. "...
Igor Paulino's user avatar
0 votes
1 answer
96 views

I am getting the answer as 4, so where am I making the mistake?

Question: In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double ...
dguy's user avatar
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-1 votes
1 answer
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What kind of a group of numbers will exhibit such property? [closed]

Let us take a set of numbers, S. For every group of any numbers taken from S, their average is always an integer. What property or pattern do the numbers of S will definitely follow?
Navin Kumar's user avatar
-1 votes
2 answers
62 views

Wikipedia: Convex combination vs weighted average

Wikipedia: Convex combination a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-...
BCLC's user avatar
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1 vote
3 answers
55 views

Why does total salary differ over 5 years if the average salary increase averages to the same?

I'm considering 2 general scenarios of both having an average salary increase of 6% over 5 years. But in the first scenario, the person ends up with a lower total salary compared to the second ...
sheavictoria's user avatar
1 vote
1 answer
43 views

Ensemble average under integral sign

Let's say there is some $v(t) = \int_0^t f(t) dt $. How can I take an ensemble average of this quantity? Is $\langle v(t) \rangle = \int_0^t \langle f(t) \rangle dt$? How does the average goes inside ...
Brownian_Motion's user avatar
5 votes
5 answers
669 views

Why is my weighted average much higher than the normal average?

For my profession I have to calculate the weighted average number of days it takes a business to review contracts. The count of each contract types reviewed is the weight, and the sum of days it takes ...
Caitlin B's user avatar
0 votes
1 answer
18 views

Variance of averaged samples from a Gaussian distribution

Let $X = N(\mu,\sigma^2)$ Let $y_n$ is the $n^{th}$ sample drawn from $X$. Let $Z_n = \frac{\Sigma_{i = 1}^{i = n}y_n}{n}$ . What is the variance of $Z_n$. My try: $A = P_1 + P_2$ with $P_i = N(\mu_i,\...
Vinod's user avatar
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1 answer
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Expected value and average value problem

One has a very large batch of tablets. The weight (unit: gram) of a randomly selected tablet can be accurately considered as a normally distributed random variable X with mean μ and standard deviation ...
Need_MathHelp's user avatar
3 votes
1 answer
92 views

What is the formula that connects the average distance to the nearest point and the average number of points per unit volume?

We have an infinite 3D space with points randomly disseminated inside it. Let $p$ be the average number of points per unit volume. Let $d$ be the average distance to the nearest point. What is the ...
Omega Force's user avatar
0 votes
0 answers
21 views

Average of multiple normally distributed Datasets

Heyo everyone :) My math education mostly stopped after school, so please bear with me while I try to describe my issue as best as I can: In a game I play there's a clear measure for your performance ...
infinitejumpingfrogs's user avatar
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0 answers
34 views

How to report the accuracy of the average of multiple sensors?

I am measuring the temperature of a metal plate using 4 thermal sensors. The sensor used is specified to have an accuracy of ±0.1°C. If I have for example those readings: The average of all sensors ...
Francois's user avatar
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1 vote
0 answers
35 views

Splitting the barycenter of a curve

Definitions Consider a generic smooth closed curve $c(t):[0,1]\mapsto \mathbb{R}^2$ and define its barycenter $g$ as \begin{equation*} g \triangleq \frac{\int_0^1 c(t)\,\lVert \dot{c}(t)\rVert \text{ ...
matteogost's user avatar
2 votes
1 answer
38 views

Generalization of Geometric Mean, Standard Deviation, etc.

The geometric mean can be thought of as the exponential of the arithmetic mean of the logarithms of your dataset $\{a_i\}_{i=1}^n$: $$GM = \exp\left(\dfrac{1}{n}\sum_{i=1}^{n}\ln(a_i)\right)$$ ...
Patch's user avatar
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-1 votes
2 answers
56 views

Average item cost [closed]

So let's say I can open up crates that have balls in it, but the amount of balls received from each crate has different percentage probability. As shown bellow: ...
Jason C's user avatar
3 votes
2 answers
159 views

Stochastic average of a differential equation is not the same as average of its solutions

Assume a static (time-independent) random variable $r$ for which we know its probability distribution $P(r)$. Consider this to be a Gaussian distribution, such that $\langle r \rangle=0$ and $\langle ...
J.Agusti's user avatar
  • 155
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0 answers
76 views

combine multiple weighted averages

Suppose there is a dataset $X = [x_1, \cdots, x_n]$ where each element $x_i$ has a set of features (weights) $A_i = [a^1_i, a^2_i, \cdots , a^k_i]$. We then can have a multiple weighted average ...
goku7489's user avatar
4 votes
0 answers
162 views

What type of mean satisfies "average rate of change is the mean of derivatives"?

From observations, for quadratic functions, the average rate of change in $[a,b]$ is the arithmetic average of the derivative evaluated at $a$ and $b$. $${\rm{Avg. ROC}_{[a,b]}}=\frac{f'(a)+f'(b)}{2}\...
sreysus's user avatar
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-1 votes
1 answer
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Folland chapter 3 exercise 22 Hardy-Littlewood maximal function and maximal theorem

Following is a question and it's solution from folland's real analysis chapter 3 exercise 22. Q22. If $f \in L^1\left(\mathbb{R}^n\right), f \neq 0$, there exist $C, R>0$ such that $H f(x) \geqq C||...
Siddharth Prakash's user avatar
1 vote
2 answers
71 views

Birthday problem: how to show the scaling with $1/N^2$?

Suppose there is a sequence of$N$ numbers $x_1, x_2, x_3, ... x_N$. There are then gaps $|x_i - x_j|$, and the minimum gap: $\delta (N) = \text{min}_{i \ne j \le N} \{ | x_i -x_j | \}$. Let the mean ...
Nigel1's user avatar
  • 655
0 votes
0 answers
16 views

What is the average of the squared ratio between the 2 norm and the max norm of a vector of iid gaussian variables?

I originally wanted to compute the following quantity $$ \langle v_{\max.}^2 \rangle_{S_d} = \left\langle \frac{\| x\|_{\infty}^2}{\|x\|_2^2} \right\rangle_{\mathcal N_n(0,1)} $$ which is the average ...
Piano Piano a Tratti Forte's user avatar
2 votes
1 answer
52 views

What is the intuition behind the single-pass algorithm (Welford's method) for the corrected sum of squares?

The corrected sum of squares is the sum of squares of the deviations of a set of values about its mean. $$ S = \sum_{i=1}^k\space\space(x_i - \bar x)^2 $$ We can calculate the mean in a streaming ...
Foobar's user avatar
  • 175
0 votes
1 answer
57 views

Getting the right average rate of growth

I am trying to get the average rate of growth across a series of numbers that will lead to the same sum as the discrete rates of growth. For example, if I have 1 unit at $t=1$ that grows at 2%, then 3%...
Shri's user avatar
  • 11
0 votes
1 answer
38 views

How do I go from an infinite amount of instantaneous rates to an average rate?

I have a function that gives me rate at a point (the derivative) and I have a value for average rate that was experimentally calculated. How would I go about creating an expression to solve for a ...
DaBest Gamer's user avatar
3 votes
1 answer
69 views

what more can I say using Sturm's comparison theorem?

Can I use Sturm's comparison theorem to say something about the average? Let $f(t)$ be a continuous function such that $\lim_{t \to \infty } f(t) = \infty$. Let us consider the following function $$ \...
alejandro's user avatar
  • 123
0 votes
0 answers
29 views

Mathematical Notation for mean of a variable in a class

I would ask for your help. How can I write down in mathematical notation the average for a specific feature that has a specific class. For example, in a dataset with two features: a continues HEIGHT, ...
GeorgeStu's user avatar
1 vote
1 answer
81 views

You're constantly drawing a random integer among {-1, 0, +1}, and adding the results. On averege, how many tries for a positive number result?

You have a randomizer that gives you either -1, 0, or +1. You start with 0, draw a random number, and add it to your total. On average, how many numbers you have to draw before you have a positive ...
Ellye F. S.'s user avatar
6 votes
2 answers
213 views

under which conditions $\lim_{t\to \infty} \frac{1}{t}\int_0^t f(s)ds$ implies $\lim_{t\to \infty} f(t) $

I am interested in knowing under which conditions $\lim_{t\to \infty} \frac{1}{t}\int_0^t f(s)ds$ implies that $\lim_{t\to \infty} f(t)$ exist. It is known that $\lim_{t\to \infty} \frac{1}{t}\int_0^t ...
alejandro's user avatar
  • 123
1 vote
3 answers
83 views

What is statistically more accurate - the average of a dataset of calculated concentrations or the sum of the total mass divided by the total volume? [closed]

Hopefully an easy question to answer. But if I have a series of five water samples, each sample is a different volume with a different number of plastic particles contained within. I can calculate the ...
E Wisniewski's user avatar
1 vote
1 answer
29 views

Weighted Average Over Time for Data Projection (aka Weighted Moving Average) - Mathematically Correct Way to Determine Weights?

Consider the following data set: Say graduation rates for a specific college's undergraduate program that are the following: Year # of Graduates Year 11 10,500 Year 12 10,750 Year 13 11,000 Year ...
SEStudent's user avatar
3 votes
0 answers
73 views

Conjecture about average cluster size in a prime-like sequence

Consider the sequence $u_n=n^a+p_n$, where $a$ is a real constant and $p_n$ is the $n$th prime. Write down the terms in $u_n$ increasing from left to right. From each term, draw a line segment ...
Dan's user avatar
  • 25.8k
0 votes
1 answer
38 views

Derivation of the effective path length

I am trying to understand the derivation of the effective path length $d_{eff}$, which is the average length $L$ of the intersection between the rain cell of length $d_{0}$ and path $d$ shown below ...
radastro's user avatar
0 votes
0 answers
45 views

Normalize data around a specific value

I am having trouble to solve a problem about normalization around a specific value. Let's say i have this data below: ValueA ValueB Division (A/B) Gap (Division - 0.625) 10 10 1 0.375 10 16 0.625 0 ...
romainL's user avatar
3 votes
2 answers
99 views

If the average of the series is an integer, prove that there exists a number in the sequence that does not appear more than $n$ times.

We consider a sequence of $6n+5$ numbers $(n \in \mathbb{N})$ all belonging to the set {$4, 5, 6, 7$}. If the average of this series is an integer, prove that there exists a number in the sequence ...
Kokos's user avatar
  • 418
1 vote
0 answers
62 views

Arithmetic mean of proper-class-sized ('unsetly') list of real numbers

Suppose I have this list $1, 1, 1, 1, 1…$ with $\bf{Ord}$ (the proper class of ordinals) number of $1$'s. Then would the average (arithmetic mean) of the list be $1$ because there is literally no ...
3-1-4-One-Five's user avatar
0 votes
2 answers
95 views

A tricky question on kinematics asked in a competitive exam

So I found this rather ambiguous question based on kinematics from a competitive examination, the question with options is - A car travels in such a way that its velocity becomes twice the previous ...
Nirmish Sarmalkar's user avatar
1 vote
1 answer
135 views

Determining the average rate of change of a product's price over time

I'm currently studying a model that describes the cost of 1 kg of a product $p$ in dollars over time, given by the equation $$\frac{d^3p}{dt^3} + a\frac{dp}{dt} = b,$$ where $a = 9[year^{ - 2}], b = ...
Ivn's user avatar
  • 119
0 votes
0 answers
59 views

Characterize a function given the average and the median

How to (1) obtain some examples for an $f$ function and/or (2) characterize the whole set of $f$ functions which has the following properties given $m$ ($\leftarrow$ the median) that $0 < m < ...
Bálint Sass's user avatar
0 votes
1 answer
42 views

The relative difference of averages gives different result than the Average of relative differences

Say I have these values : Value 1 Value 2 Absolute difference (Value 1 - Value 2) Relative difference (Value 1 / Value 2 - 1) 0.80 0.30 0.50 167% 0.75 0.20 0.55 275% I'm interested in calculating ...
pollytatouin's user avatar
3 votes
4 answers
365 views

What is $\lim_{x\to\infty}\frac{\int_{0}^{x}\cos\{t-\cos t\}dt}{x}$?

I want to find a closed form for the average value of $\cos\{t-\cos t\}$ where $\{n\}$ denotes the fractional part of $n$. I do not have experience finding an average value over an infinite domain but ...
Dylan Levine's user avatar
  • 1,698
0 votes
2 answers
45 views

Average value of a function over some given interval

I was learning about simple harmonic motion from YouTube and in one of the lectures the teacher introduced to the formula for the average value of a function I know that formula for the average value ...
Anshu Gupta's user avatar
1 vote
0 answers
23 views

Help with formula to calculate "earnings"?

I'm looking to calculate earnings on a writing platform, based on a variety of metrics. Unfortunately I suck at math, and am unable to come up with the exact, proper formula to find an average. ...
FMB's user avatar
  • 111
0 votes
0 answers
58 views

Average of two discrete random variables

I have this graph B<-A->C and I have the joint probability distribution of A and B , P(A,B), and the joint probability distribution of A and C, P(A,C). I want to compute the average of B and C. ...
Moh's user avatar
  • 21
1 vote
2 answers
99 views

Inequality involving average value of a function

Consider the Integral $$\frac{1}{r}\int_{0}^{r}f(x)dx.$$ My observation, after testing several elementary functions, is that if $f(x)$ is a decreasing function, then $$f(r)\leq\frac{1}{r}\int_{0}^{r}f(...
mersa's user avatar
  • 11
0 votes
0 answers
84 views

Calculating weighted averages in ranking task

I have a set of eight principles and have been tasked with working out what the top five preferred principles are. In a series of interviews, participants were asked to rank their top five, with 1 ...
atem634's user avatar

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