# 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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{ ...
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### 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 $\{a_i\}_{i=1}^n$: $$GM = \exp\left(\dfrac{1}{n}\sum_{i=1}^{n}\ln(a_i)\right)$$ ...
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### 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: ...
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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. ...
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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(...