The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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97 views

Average of an exponential over Dirichlet probability distribution on the (n-1)-simplex

Any idea how I can solve this integral for arbitrary integer $n$ ($n \geq 2$) with real non-negative coefficients $\{s_i\}_{i=1,..,n}$: $I(s_1,...,s_n):= \int_0^1 dx_1 ...\int_0^1 dx_{n}\,\, e^{ ...
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1answer
26 views

cal average speed

the following table represents the number of miles traveled per day by a hiker on his week-long excursion. Find the hiker's average speed in miles per day in the latter half of the week(days 4-7) Day ...
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1answer
52 views

The Average Speed of an object

I'm pretty sure this has more to do with fundamental Math than Physics and that is why I'm asking this here rather than Physics.SE Imagine some object travelling along a straight path from point $A$ ...
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2answers
39 views

Inverse Percentage.

Sorry for asking this foolish question. Here is the data i have. I purchased the product as $5 and additional fee is 2%. So Here is the total dollor ...
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1answer
22 views

Set of Points into Two Groups with Same Average?

What kind of algorithm using MATLAB or done by hand will allow someone, given a set of data points, to divide them into two groups with as close of an average as possible?
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42 views

Doubt on an Adaptive algorithm used for Voice Activity Detection

Recently in the task of implementing a adaptive energy algorithm for VOICE ACTIVITY DETECTION ,i came across an algorithm which is working properly and well but the problem is i am not able to ...
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0answers
31 views

Predicting future use.

I am in need of a formula that I can use to predict future use of a specific unit. You can think of the unit as how much electrical current is flowing in a wire. It varies a lot during the course of ...
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0answers
19 views

Average of several harmonic means

I would like to know if it is possible to calculate the mean and the standard deviation for several harmonic means. More specifically, I have 20 harmonic means. And every harmonic mean was calculated ...
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0answers
27 views

Are there any side effects of changing an alpha value on an existing exponential moving average?

I am designing an adaptive smoothing filter using an exponential moving average. However, instead of using a fixed alpha value I would like to use an incrementally increasing alpha value so that the ...
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1answer
302 views

Mean/ Expected Value of $X^4$

$\def\Var{\mathop{\rm Var}}$Can anyone help me prove that Expected Value of $X^4$ is $3\Var(X)^4$, if the Expected Value of $X$ is zero and $\Var(X)$ is the Variance of $X$? Thanks!
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3answers
41 views

Average value of recurrent function.

Given a function f(x) = a*f(x-1) where a is a number between 0 and 1, what is the average value of ...
1
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0answers
66 views

Game of bullets

Lets say with have a game with 10 targets. In each turn the participant shoots X number of different and random targets, where X is a random whole number between 0 and 10 (included). Game ends when ...
0
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1answer
35 views

what “average” to use that will give the most relevant value f0r portfolio

My assignment requires me to find return on capital, industry wise for the loan portfolio classified into various industry/sector, the data fields are : ... Name of account|industry|Outstanding ...
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1answer
77 views

Geometric Mean of an Interval

Is there any way to calculate one? If it't not clear what I mean, here's an example: Starting with an initial value, keep multiplying it by some random amount on the interval [1, 2] at regular ...
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0answers
281 views

Bar Mean vs Bracket Mean

I know that the standard representation for the average of a data set: $$ \bar{x} = \frac{1}{N} \sum_{i}^N{x_i} $$ I have also ran into an average denoted as $\langle x \rangle$. This notation is ...
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0answers
31 views

Is $x_1^{\alpha_1} + \dotsb + x_n^{\alpha_n}\geq x_1^{h/n}\dotsb x_n^{h/n}$ an example of power means?

I learned here that there is a relation between weighted means of the form $x_1^{\lambda_1}\dotsb x_n^{\lambda_n}$ and $(\lambda_1 x_1^r + \dotsb + \lambda_nx_n^r)^{1/r}$, namely that the former is ...
6
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1answer
200 views

Why is the $0$th power mean defined to be the geometric mean?

Mentioned in the wikipedia article, the $0$th power mean is defined to be the geometric mean. Why is this? I understand that a convenient consequence is that the means are ordered by their exponent. ...
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5answers
141 views

How do you determine the “average” of a certain value?

I have checked out the Wikipedia article, but it's too complicated for me. Also, this definition: constituting the result obtained by adding together several quantities and then dividing this ...
6
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0answers
199 views

What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
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1answer
37 views

Statistics Range from x to y find average

The problem state that: Quantity A: The integer ages of the three children range from 2 to 13, and no two children are the same age. The average of all three children. Quantity B: 10 Compare A and ...
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3answers
55 views

Estimating $\sum_{k=1}^N a_kb_k$ given the means $\bar a_k,\bar b_k$ and determining the error

I need to calculate the following expression: $$\sum_{k=1}^N a_k b_k$$ I know the average values of $a_k$ , defined as $\overline {a_k} = {\sum_{k=1}^N a_k \over N } $ and $b_k$ , defined as ...
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1answer
23 views

What is the average value of number-range along interval?

Given a finite range of real numbers $$x = x_0,x_1,x_2,...,x_n$$ and an interpolation function $f(c), c\in[0..1]$ (such that e.g. $c(0)=x_0$, $c(1)=x_n$), and an interval $$I =[u,v], u\in[0..1], ...
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2answers
46 views

Average and aggregate values with a distribution function

I'm reading an economics paper and I'm trying to understand if a statement made by the author is an assumption or the consequence of a previous definition. The part I don't understand is the ...
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0answers
31 views

Does MACD have exact or approximate upper bound and lower bound?

A MACD is a difference between two moving averages, typically, 12-day Exponential Moving Average and 26-day Exponential Moving Average. With some stock prices, I observed that the range of there MACD ...
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2answers
62 views

Average Proofs, where $n\ge 2$ is greater than the average of real numbers

Prove that at least one of the real numbers $a_1; a_2;... a_n,$ where $n \ge 2$, is greater than or equal to the average of these numbers. I'm stuck on how I am supposed to prove this. Honestly ...
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1answer
29 views

Probability question help

A company that sells annuities must base the annual payout on the distribution of the length of life of the participants in the plan. Suppose the distribution of male participants' lifetimes is ...
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1answer
96 views

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need? I may not be using the correct terminology so here's a graph: Based on this, if you ...
2
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1answer
69 views

Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
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2answers
275 views

find new average if removing one element from current average

Ok, so say that I have a current rating average: 3.3/5 Now I want to say to remove a rating of 4. How do I find the new average? Or is this even possible?
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0answers
61 views

Difference between $\frac{1}{n} \sum_{i=0}^n \frac{b_i}{a_i+b_i}$ and $\frac{\sum_{i=0}^n b_i}{\sum_{i=0}^n a_i + b_i}$

Consider scenario like this: each user can add movies. each user can rate movies he added. I want to know how many movies average user has unrated (as in average percentage). Let's translate this ...
0
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0answers
49 views

About a special way to find the average waiting time to get a sequence

A friend of mine taught me the following question: You have a coin. When you toss it up, heads you note $1$, tails you note $0$. Then, tossing it up repeatedly, let's find the average waiting time to ...
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2answers
46 views

Expected average of number of tiles empty

I have a grid of 3x4 and every tile on the grid has a corresponding chance of being empty. This chance is given. For example, consider the following grid: $$ \frac{14}{15} \frac{1}{3} \frac{8}{13} ...
2
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3answers
65 views

Why should ${\sum_1^n {s_i} \over \sum_1^n {t_i}} = {n \over \sum_1^n{t_i \over s_i}}$? (harmonic mean)

I realized it reading about computer performance. This identity is presented there with words: dividing total distance by total time, you arrive at average execution rate on the left. On the right, ...
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2answers
69 views

Bringing numbers in a set closer together

I'm trying to express the relative scale of items compared to an "average" scale for all items in the set. This produces values like { 0.5, 1.8, 0.3, 1.2 ... } I then wish to use this number to ...
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1answer
38 views

For N-day moving average, how is N parameter called?

I'm looking for a good name for the variable. Average window length? Sounds like a term for a glass cutter.
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1answer
37 views

Average amount needed for x number of months remaining

I'm trying to calculate the average amount of profit needed to hit a milestone based on the number of months remaining. So let's say the goal is £1,000 and there are 5 months left. If I have £400 ...
2
votes
0answers
58 views

The angle of an average rotation is $126.5^\circ$?

In the paper "Applications of Quaternions to Computation with Rotations" by Eugene Salamin, 1979 (click here), they get 126.5 degrees as the mean value of the rotation angle of a random rotation (by ...
1
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1answer
429 views

Weighted Average of Percentage Increases

I believe I have quite a simple problem, but want clarification on whether it is the best method to use. Say I have have insurance line, and the net income (£) from this business for 2011, 2012, 2013 ...
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2answers
647 views

How to calculate weight of positive and negative values.

We have used formula formula to calculate weight as, $$ w_1 = \frac{s_1}{s_1 + s_2 + s_3};$$ $$ w_2 = \frac{s_2}{s_1 + s_2 + s_3};$$ $$ w_3 = \frac{s_3}{s_1 + s_2 + s_3};$$ However, their is ...
0
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2answers
146 views

Calculate the average sales per day in 2010.

In 2005, Company K was 730 000 units of the car market. Total sales is 50% of the total cars sold in 2010. Calculate the average sales per day in 2010. Calculation: 1) 50/100 x 730 000 2) 730 000 x ...
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votes
2answers
69 views

What is the calculation for an average speed? [closed]

George is driving 100 miles in 1 hour and 30 minutes. What is the calculation involved when looking for an average speed of George? Answer: Divide 100 by 1.5 How to make the calculation for the ...
5
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1answer
146 views

continuously averaging a stream of numbers

Ok, so I'd like a little help with the mathematical theory behind something I'm doing in a program. I've got a stream of numeric inputs, and I need to find the average of all the numbers in this ...
29
votes
2answers
2k views

What's the mean of all real numbers?

At first, I had thought the average must be zero, since for every positive number there's an equal magnitude negative number to cancel out the positive number's effect on the average, leaving only ...
0
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1answer
111 views

average/weighted average within Excel

5 star 128 4 star 17 3 star 10 2 star 2 1 star 14 Average stars 4.42 How many more 5 stars would I need to get ...
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0answers
62 views

How to measure the time-decayed rate of independent event

I have events arriving in a software system at a variable rate. Imagine these events are, say, hits on a website. I'd like to periodically report on the rate of arrival of events over a number of ...
8
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5answers
365 views

Puzzle in Percentages

Okay, this is a real-time problem. The following is a picture of Customer satisfaction rating, which was displayed next to an item in an online shopping website. Satisfied customers click the ...
0
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1answer
79 views

different types of Averages : prove there is an inequality between different averages

This is something I have been curious based on observations I have made by analyzing data from the energy industry. The context is you have monthly data for energy used per month and the cost per ...
4
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2answers
196 views

If I put $M$ balls into $N$ boxes at random, what is the average number of balls in the boxes that are not empty?

I have a very brief question: if I put $M$ balls into $N$ boxes at random, what is the average number of balls in the boxes that are not empty?
2
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3answers
63 views

What is the mean score for the $20$ rolls?

A fair die is rolled twenty times. The results are shown in the bar graph. What is the mean score for the $20$ rolls?
2
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2answers
438 views

Way to aggregated percentiles

I want to have information of http response times. The average, 95 and 99 percentil. All the response times are collected in each web server, and every second is sent back to a central server that ...