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.

Filter by
Sorted by
Tagged with
1
vote
0answers
37 views

If the product of $n$ distinct positive integers is $n^n$. What is the minimum value of their average if $n = 6$?

As $n=6$, then $n^n = 6^6 = 46656$ and I was able to break it into the product of lowest positive integers in the form as below :- $n^n = 6^6 = 46656 = 1 \times 4 \times 6 \times 9 \times 12 \...
1
vote
1answer
58 views

Average of the Averages.

From $10$ numbers $a,b,c,...j$ all sets of $4$ numbers are chosen and their averages computed. Will the average of these averages be equal to the average of the $10$ numbers? I tried analyzing smaller ...
1
vote
1answer
40 views

Edwards Penney, Calculus: Early Transcendentals, 7th Ed., Ch 5.6 Ex 36: how is the integral in the solutions manual calculated?

In the Calculus book "Calculus: Early Transcendentals" by Edwards and Penney, 7th Edition, in the chapter on the fundamental theorem of calculus, there is an exercise (Chapter 5.6, exercise ...
0
votes
0answers
25 views

Computing average return on negative returns (gemoetric mean)

So let's say a portfolio created a loss (leveraged portfolio) of $104\%$ in six months. What would be the average return be per month? My guess would be $(1 + 1.04)^{\frac{1}{6}} = 1.126$, so my ...
0
votes
2answers
22 views

How do I convert an array of numbers from an old range to a new range, where the highest valued number is 100 and the lowest valued number is a 0?

I am trying to develop weights for a mapping application of mine. I know it's a bit of a weird question, but say we have an array of some values like [1, 5, 7, 9, 3] I want the converted array to have ...
0
votes
1answer
203 views

How to define a measure similar to Lebesgue, for the average of any function, in a more rigorous manner?

Intro I'm an undergraduate enrolled in an online university. Currently, the highest course I've taken is Intro to Advanced Math. Despite being a beginner, I read into other advanced topics. Yet, ...
0
votes
1answer
66 views
5
votes
1answer
40 views

Approximating the average of a list consisting of real numbers

Given a list of real number $(a_1, a_2, \ldots,a_n)$ we are interested in the average $\mu = \dfrac{1}{n}\displaystyle\sum_{i = 1}^{n}a_n.$ You are given a simple probabilist algorithm that ...
0
votes
1answer
18 views

Average Employment Time (Poisson Distribution)

I'm working on the following problem: I'm having a real hard time finding any information regarding of how I should approach the problem. From what I see, am I correct that this might require the ...
0
votes
0answers
21 views

How much did each item contribute to the month over month rate change?

I am observing a $2.5$pp increase in discount from December to January. How can I calculate how much the increase in the device discount and how much the increase in battery discount contributed to ...
0
votes
0answers
20 views

Trick for solving an integral

I am trying so solve a practical problem (i.e. not sure if my questions has any nice solution), and I reached a point where I need to solve an integral of the form $\int_0^Tf(t)e^{at}dt$, where $f(t)$ ...
0
votes
1answer
27 views

How do you calculate the impact of each item contributing to the total discount?

I have 2 items: Devices and Batteries and I am observing the revenue I get from both over 2 months: in December the Revenue for the devices was 5.1Mio in $ and Discount 292K, January (6.17Mio and 482K)...
2
votes
1answer
63 views

different types of averages and converting them to work with functions.

I've been thinking about different ways to average a set of numbers the two that I know are the geometric mean and the arithmetic mean I thought of a knew type of Mean. where instead of adding or ...
0
votes
0answers
24 views

average on different quantity [duplicate]

Note: please English is not my first and here I saw people use hard words I can not understand. please consider simple words, thank you. If I bought an item 3 times at different prices. the average ...
0
votes
0answers
38 views

Average Value for non-differentiable function?

Surprisingly, I could find no answers for this on either YouTube or the internet. I'm looking for the average rate of change on the interval $[-1,3]$ of the function: $$f(t)=6t^2+\frac{4}{t^2}$$ Now, ...
1
vote
1answer
50 views

Average distance between a point and the center of a unit square (Why my answer is wrong?)

This question is from the MIT OCW course on Multivariable Calculus, and that particular question has been answered in this forum before. What I'd like to know is where is the mistake in my attempt to ...
-1
votes
0answers
29 views

weighted average vs normal average - I'm suddenly confused!

If I have a list of numbers like: 50, 30, 20 Isn't average = weighted average? The answers seem to be the same.. Also, for weighted average, what are the weights in this example? is it all 1? Please ...
1
vote
1answer
35 views

Average of all $a_n$ where $a_0$=1, $a_{n+1}=\omega^{a_n}$, and $\omega=\frac{\pi i}{\ln(2)}$

Essentially, I've noticed that tetrations of $\omega=\frac{\pi i}{\ln(2)}$ seem to converge on a cycle of three fixed points. Specifically, if $a_0$=1, and $a_{n+1}=\omega^{a_n}$, then we find $$n\...
1
vote
0answers
33 views

What is the average distance between points in a circle that lies on a sphere?

For a sphere of radius R with a circle of intrinsic radius r on it, what would the average intrinsic distance be between points in that circle? I'm as interested in approaches/methods as I am in the ...
0
votes
0answers
13 views

How do I calculate the median from a histogram with uneven class width?

There a question in my textbook which says: The histogram gives information about the times taken, in minutes by a group of students to travel to school in one week (next to the question there is a ...
0
votes
1answer
13 views

How to get an average number of free consumables provided a chance not to consume?

Example: I have n consumables and a probability $x_p$ to not use a consumable without losing it, how many free consumables $f(x)$ do I get on average? My guess is that if you convert the probability $(...
0
votes
0answers
13 views

Testing an Average Rate

Suppose that I want to test the claim that the average monthly unemployment rate in France is 9%. I have three years worth of data, from 01/2017-12/2019 (i.e. 36 observations). Should I be testing the ...
0
votes
1answer
24 views

Calculating weighted average between a number and a percentage

How do I calculate the weighted average between a percentage and a number? For $120\%$ and $88$, assuming that $120\%$ weighs $60\%$ and $88$ weighs $40\%$. For context for 120% it is based off this ...
3
votes
2answers
109 views

Which of these is the correct average rate of change?

The question is to find the average rate of change of $2000e^{0.21x}$ between $2$ and $5$? I found the derivative of the equation ($2000e^{0.21x}$) and averaged them, I found the average rate of ...
0
votes
1answer
15 views

How is the exponential moving average calculated?

For example, imagine I have the following data set $V =\{10,12,11,10,13,14,12\}$. How could I calculate the EMA of the data set at a given index? With $\alpha = 0.2$ I believe the equation is as ...
0
votes
0answers
14 views

What's the best way to calculate the average wind speed?

I am randomly generating wind speed for the X and Z axes. Let's say I have that the wind is blowing X MPH in the north direction and Y MPH in the east direction. I want one final value for the wind's ...
0
votes
0answers
24 views

Find mirror value of an alternating function.

Let: $$g(2n) = f(2n) + c$$ $$g(2n-1) = -f(2n-1) + c$$ $$n \in \Bbb{N}$$ Known: $g(x)$ Unknown: $f(x)$, $c$ $$c = ?$$ Image: How to calculate $c$, is there any useful math property ? I will apriciate ...
0
votes
1answer
36 views

Is it really easier to decrease your overall grade in a class than increase it?

I was thinking about how grades work. Obviously most people’s grades are weighted, each type of assignment holds a different value and exams usually count for the most. People always complain about ...
0
votes
0answers
46 views

Weighted quadratic mean inequality

It is very well-known that given positive real numbers $a,b$, then $$ \dfrac{a+b}{2} \le \sqrt{\dfrac{a^2+b^2}{2}} , $$ and equality holds if and only if $a=b$. Is there an analogous "weighted&...
1
vote
2answers
22 views

average proportions over time

Let us say I have a number of events per week over some time periods. During each week a proportion of these events are important (important_events_per_week/number_of_events_per_week). The ...
1
vote
0answers
19 views

calculate average percentage of measurements over time

Let us say I have weekly measurements over time and I have a target measure for each week. Is it too naive to calcuate the relative difference: ...
0
votes
0answers
32 views

Average value of a set

Suppose I have a set $ F=\left\{ x\mid x\in\mathbb{R}^{N}\cap Ax=b\cap\left(0\leq x\leq1\right)\right\} $ where $A\in\mathbb{R}^{M\times N}$ and $b\in\mathbb{R}^{N}$. If every value in the set is ...
0
votes
1answer
13 views

Backing into mixture from weighted average of 2 items

Item1 Price: $1 Item2 Price: $2 WAP (weighted average price): $1.5 Correct Answer: 50% of item 1 and 50% of item 2 would have a WAP of $1.50 But how would I calculate the percentage of each needed to ...
2
votes
1answer
112 views

Can two sets $A,A'\subset\mathbb{R}^n$ have the same measure but different expectation?

I have three 'simple' questions regarding measure theory. For every measurable set $A\subset\mathbb{R}^n$, we define the avarage value of $A$ (denoted as $\mathbb{E}[A]$) by \begin{gather} \mathbb{E}[...
3
votes
4answers
76 views

Probability St Petersburg Game

I am reading a book on probability and there is an interesting chapter on the St Petersburg game - where a coin is flipped until a head is landed and the prize is £2 if there is a head on the first ...
0
votes
0answers
9 views

How to calculate the percentage of change between two dates without being fooled by trend effects?

I have a dataframe of sales per store and per item between month 0 and month 33, these sales represent a non-stationary time series. I want to calculate how much these sales are increasing. But I don'...
0
votes
0answers
22 views

Is it possible to express an infinitesimal area as a sum of squares?

I came across a question which was asking the center of mass of an area, the centroid. The proposed solution uses weighted average, the formula is that given a planar region, the x and y coordinates ...
0
votes
1answer
46 views

Proof that the phase of the average of unitary complex numbers is the average phase

I'm quite struggling with the following problem: -Prove that if \begin{equation} re^{i\psi} = \frac{1}{N}\sum_{j=1}^N e^{i\theta_{j}}, \end{equation} then $\psi = \frac{1}{N}\sum_{j=1}^N \theta_{j}$, ...
1
vote
1answer
52 views

Integers of a series

The first $n$ consecutive positive integers in a series are $1, 2, 3, 4...n-1, n$. The integers $a, b, c, d$ are removed from the list. $100<a<b<c<d$ and at least $3$ of $a, b, c, d$ are ...
1
vote
2answers
48 views

Exponentially weighted average, sum of weights

I'm just wondering how to actually prove that the weights of an exponentially weighted average sum to 1, like $(1-\alpha)^n + \displaystyle\sum_{i=1}^n \alpha (1-\alpha)^{n-i} = 1$ where $\alpha \in (...
0
votes
0answers
36 views

How to take mean of n-dimensional vector along a given axis?

I'm trying to take the mean of a given n-dimensional vector along one of its axes. For example, $\mu_2\begin{bmatrix} 1 & 2 & 2 \\ 2 & 3 & 4 \\ 4 & 4 & 2 \end{bmatrix} = \...
1
vote
1answer
30 views

Sigma of 50 element sample vs sigma of the average of 5 samples of 10 elements

I would like to understand a statement I found on a book concerning the explanation of confidence interval which is not clear to me. We have two different situations and I would like to understand if ...
3
votes
2answers
194 views

How can an average decrease in numbers show up as an average percentage increase?

In the list below: the first column shows the population the second column shows the number by which the population has increased (so the total new population in the first row would be 27312). the ...
1
vote
1answer
28 views

How to compute/estimate the probability of the mean value of x results, if each one of the results has its own probability

I use a neural network to classify the sentiment of some articles per day. Possible results are [1,2,3,4,5] (1=very negative, ..., 5 = very positive). Using one article as input the network gives me ...
2
votes
1answer
115 views

Simplify this statistical average

I have a quantity $\tau$ given by: $$ \frac{1}{\tau} = \frac{1}{\tau_1}+\frac{1}{\tau_2}+\frac{1}{\tau_3} $$ where $\tau_1$, $\tau_2$ and $\tau_3$ are some constituent quantities. Now these $\tau$'s ...
1
vote
0answers
50 views

Average distance between points

If there were a square field that is $x$ km wide and long, and there are $y$ objects in the field, is there a way to calculate the average distance between each object? I tried $\frac{x}{\sqrt{y}}$, ...
6
votes
2answers
109 views

$ \sum_{i=1}^{10} x_i =5 $, and $ \sum_{i=1}^{10} x_i^2 =6.1 $ ; Find the largest value of these ten numbers [closed]

Ten non-negative numbers are such that $ \sum_{i=1}^{10} x_i =5 $, and $ \sum_{i=1}^{10} x_i^2 =6.1 $. What is the greatest value of the largest of these numbers? It presents a lot of confusion to ...
0
votes
1answer
27 views

Average of middle number [closed]

I was doing a question on average and the question was that - If the average of 1st 12 number is 10.8, average of 1st 6 number is 10.4 and the last 6 number is 11.5. Find the 6th number. Now according ...
1
vote
1answer
30 views

How is the averaging of this stochastic process determined?

I am reading a physics paper dealing with a random fluctuation $R(t)$ satisfying: $\langle R(t)\rangle = 0$. $\langle R(t) R(t')\rangle = \delta(t - t')$ where $\delta$ is the Dirac-delta function ...
1
vote
1answer
102 views

A little's law question to find average of the customer in some time

If shoppers enter a store at an average rate of $r$ shoppers per minute and each stays in the store for average time of $T$ minutes, the average number of shoppers in the store, $N$, at any one time ...

1
2 3 4 5
28