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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2
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2answers
52 views

How would I apply an Exponential Moving Average to Quaternions?

I'm trying to filter positional and rotational data using an Exponential Moving Average (EMA) filter. This has worked without issues for positional data (3D vectors) but I can't figure it out for ...
0
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0answers
26 views

Expectation of Gaussian RV & an arbitrary function

I saw in a paper (https://www.princeton.edu/~wbialek/rome/refs/bialek+ruyter_05.pdf Eq.37) the following identity: where the <.> operator refers to a population average. No source or ...
0
votes
1answer
24 views

Why are there these patterns in these pathtraced images?

I've written a path tracing renderer for a technology class, and, while examining the histograms of the resulting images, I found a weird wavy pattern. The resultant image is the average of many ...
0
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1answer
25 views

Why these two average results a diferentes values?

(12 + 18 + 5) / 3 (elements) = 11,67 and (12 + 18) / 2 (elements) = 15 5 / 1 (element) = 5 (15 + 5) / 2 = 10 which one is more accurate? 11,67 or 10 ?
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0answers
11 views

Function For Calculating Average Excluding Outliers

I'm looking for a function that will let me take an average and exclude outliers. Basically something where: 1, 2, 1, 2, 7 Would average out to 1.5. Would that be along the lines of standard ...
0
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0answers
10 views

Calculate weighted average rate based on time

I'm trying to calculate the average consumption rate to be displayed by a computer program. Currently the average consumption rate is a cumulative average calculated by total consumption divided by ...
1
vote
1answer
17 views

Averaging data with different weights, and interpreting the results

I am trying to understand how to average certain data, interpret the result of that, and potentially convert the results to percentages. I have four categories for the data: 1: (0-50%): Not Well ...
0
votes
1answer
21 views

Which of arithmetic, geometric or harmonic mean is the most appropriate in this case?

I have a software that periodically detects tempo out of an audio signal and I would like to compute the average tempo out of all the generated values. Example: ...
0
votes
1answer
9 views

Averaging with a tolerance

I'm having some issues with trying to average some values. Lets say (for this example) that earthquakes are measured on a scale of 1-6. No earthquake can be stronger than a 6 and you want to calculate ...
0
votes
1answer
30 views

Find the average of this function

This is a basic algebraic question and probably a very simple one, but I'm a bit stuck. $$\matrix{f(x) = 1/x & \text{for x}\in [a,b]}$$ I've found that $\int (1/x)dx = -(1/x)$ The expression ...
1
vote
0answers
13 views

Calculating a moving average where the weight depends on the new value

I am attempting to write a small piece of code that tracks the both the time taken to render a frame in a single instance, and a more smoothed value that remains stagnant enough that it can be read by ...
3
votes
3answers
43 views

Convergence and Absolute Convergence of Arithmetic Mean of a sequence

Suppose $\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n |x_i|$ exists. Does $\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n x_i$ exist? How about the converse? My thoughts: I guess for the sequence ...
2
votes
2answers
60 views

Arithmetic Mean convergence and concave transformations

Suppose $x_i \geq 0$ $\forall i$. If $\frac{1}{n}\sum_{i=1}^nx_i$ converges as $n\to\infty$, then what about $\frac{1}{n}\sum_{i=1}^nx_i^\delta$ where $0<\delta<1$? By Jensen's inequality we ...
0
votes
1answer
17 views

Concerning averages.

Here is a simple test question: The average of 5 different integers is 33. The smallest of the 5 integers is 30. The largest of the five integers is N. How many possible values of N are there? ...
0
votes
1answer
38 views

Why is the average of the whole different to the average of the sum of the parts?

I'm a complete idiot when it comes to mathematics, so please bear with me. I have a problem. The average of the whole is different to the average of the sum of the parts. Why aren't they identical? ...
4
votes
1answer
42 views

Notation for Average of a Set?

In particular, I have some set $S = \{s_1, s_2, s_3, ..., s_n\}$ and a subset $S^\prime$, and I want to denote the average of the elements in $S^\prime$. I would generally just use ...
0
votes
1answer
14 views

On the estimation of the average of a deteriministic, scalar, real-valued function of two variables.

Suppose we have a scalar, real-valued function of two variables $F(x,y)$ where ($x$,$y$) belongs to a discrete domain $D$ of $F$, which has finite number of elements. Let $\mid D \mid$ be the number ...
1
vote
0answers
17 views

Math Average Basics, Error % calculation, and Blood Pressure.

I saw on the Olympics once when they were doing scoring for team events, that on some events the judges would take each members performance, eliminate the highest and lowest members performances, and ...
0
votes
0answers
9 views

Cumulative average of an average

I am trying to do a calculation for a stochastic oscillator on a series of stock prices in a database (SQL Server 2014). The calculation I am trying to do is as follows: Work out the lowest low for ...
0
votes
0answers
6 views

calculating a moving average rate for detecting an outbreak

I have a count for the number of occurences of a disease over a period of time. I want to set a threshold for detecting unusaul increase with a moving average. I am planning to use + 1,2,3 SD to set ...
1
vote
2answers
28 views

Adding to an average without unknown total sum

Let's say I know the following: Let A be the average value Let T be the number of values Assuming that A = 4.3 and ...
1
vote
1answer
14 views

Better Rating Result instead of Average

In my database, each item has a total_votes and total_ranking. When a user vote, I add +1 to the total votes and add its rating ...
0
votes
1answer
8 views

Continuous averaging of solar cell efficiency

I have a stream of numbers - efficiency ratio of solar cells - in range 0-100%. The efficiency is defined as (produced/expected)*100. I'm measuring the ratio every minute, and I'd like to have a ...
3
votes
1answer
75 views

What is this average called?

What is this average called? I tried Googling it but couldn't find anything about it. It's something between an arithmetic mean and a geometric mean, by which I mean you iterate both averages for two ...
0
votes
0answers
33 views

How many possibilities of sequences are there to have averages of adjecent two in the sequence will be as provided

Given: Sequence of Averages of adjecent two numbers in list i.e. (n-1) integers Output: how many non-decreasing sequences of n elements are possible? for example: Given: 2 4 Possibilities: 1> 0 4 ...
0
votes
1answer
61 views

What does this mean mathematically?

This piece of text is an explanation of item-based recommendation by Mahout (mahout-item-based-recs) Can anyone explain the meaning of 3rd line (running average means?) - for every item i that u ...
3
votes
1answer
50 views

Average distance to a random point in a rectangle from an arbitrary point

I'm interested in the mean distance between an arbitrary 2D point, $(p, q)$, and a uniformly distributed point inside a rectangle defined by the lower left and upper right vertices $(x_0, y_0)$ and ...
0
votes
2answers
30 views

Minimum Value Given Average

I am struggling with this (very embarrassingly basic) minimization problem: I have the answer, which is great, but I'm oblivious as to how to go about solving this short of using calculus. The ...
3
votes
2answers
43 views

An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$

Suppose $\mathcal{S}=\{\mathbf{x}:\mathbf{x}\in\{-1,1\}^n\}$, that is, $\mathcal{S}$ contains all $2^n$ vectors of length $n$ containing -1 and 1. I am interested in the following average: ...
0
votes
1answer
19 views

Covering deficits with values with different weights

SO I have a couple of assessments with specific weights as follows: Assignment 1: 5% => Mark 60% Assignment 2: 5% => Mark 53% Assignment 3: 5% Assignment 4: 5% Test 1: 30% => 47% Test 2: 30% ...
1
vote
1answer
48 views

Why average until $n-1 \times n \simeq \sum^{n-1} + avg_{n-1}$?

I'm newbie in math and I want to understand it: let $A = \{a_1,...,a_n\}$ why $$(\frac{1}{n-1}\sum_{i=1}^{n-1}a_i)n \simeq (\sum_{i=1}^{n-1}a_i)+ (\frac{1}{n-1}\sum_{i=1}^{n-1}a_i)$$ Exists any ...
0
votes
1answer
20 views

Selecting denominator for relative error margins

When looking at this page: http://floating-point-gui.de/errors/comparison/ there are values a, and b that are being compared ...
0
votes
1answer
21 views

How do I Adjust Dynamic Weighted Averages?

I am trying to create a formula in Excel that tries to create a weighted average score for a person. The only problem is that sometimes one or two of the components of the weighted average may not be ...
0
votes
6answers
51 views

Confusion (Averages)

I'm getting insanely frustrated with this. The average of $6$ numbers is $4$. A seventh number is added and the new average is $5$. What is the seventh number? How do I solve this algebraically? $6 ...
0
votes
1answer
15 views

Equation for the average of a known quantity of numbers

How would one express this in the form of an equation? The average of 500 numbers, each of which are between 2 and 50, is 7.5 And can it be graphed?
0
votes
3answers
40 views

Get the minimum value for multivariable

I need a way to calculate the very minimum of each variable for a grade average. Each grade variable have a weighing percentage (I don't know if it's the right term) The weighing sum must be the ...
0
votes
3answers
71 views

There are two cars…

Let's imagine a $6000 km$ stretch of road. Now, there are two cars $A$ and $B$, each with average speeds of $100km/h$ (for $A$) and $250km/h$ (for $B$) respectively. If $A$ is given a headstart of ...
13
votes
3answers
209 views

If my average speed is 50 mph, is it better to go 10% faster or 5 mph faster? (These are not the same)

BACKGROUND Suppose we have a journey between A and B where different sections of roads have different speed limits and our average speed is 50 mph. If when I repeat the journey I travel 10% faster ...
0
votes
1answer
45 views

Incremental averaging (different case)

I've seen the integer version $$m_n = m_{n-1} + \frac{a_n-m_{n-1}}{n}.$$ But how do I calculate it where there are amounts, which is $$A=[3, 5, 4]$$ and the corresponding quantities $$Q=[1.5, 2.5, ...
0
votes
1answer
43 views

alligation problem

Ravi lends Rs 3600 on simple interest to Harsh for a period of 5 years. He lends a part of the amount at 4% interest and the rest at 6% and receives Rs. 960 as the amount of interest. How much money ...
1
vote
3answers
47 views

Mean of a vector

Be a set of numbers $v=(a_1, a_2, \ldots, a_n)$ I want to form the following average vector $\mu = (\frac{\sum a_i}{n}, \frac{\sum a_i}{n}, \ldots, \frac{\sum a_i}{n})$. If I do it iteratively step ...
1
vote
1answer
64 views

Maximum and minimum average question

During a cricket match, India playing against NZ scored in the following manner: Partnership | Runs scored 1st wicket | 112 2nd wicket | 58 3rd wicket | 72 4th wicket | 92 5th wicket | 46 6th ...
1
vote
1answer
38 views

problem in understanding overall change in average

The average weight of 5 men is decreased by 3kg when one of them weighing 150kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the ...
0
votes
0answers
22 views

higher order schemes or curvature to be smoothed

I want to calculate the radius of curvature of a meandering river. I have done a first estimated using a tool in arcgis. These are the results. The values of -99999 are recorded for points of no ...
1
vote
2answers
38 views

Estimated wait time for a library book

A library has 20 copies of a book that circulates for 3 weeks. All copies are out and there 40 people on reserve ahead of me. How do I estimate the wait time?
0
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1answer
32 views

Basic algebra problem for weighted averages

This question has me completely stumped for some reason, I would appreciate a bit of help. If you have 20 pounds of coffee for $1.80 a pound And then add X amount of coffee for $1.44 a pound How ...
0
votes
1answer
20 views

Mean of a discrete function

I have a set of finite variables (~20) which when plotted are forming a decaying exponential function. I want to know is there a better way to calculate the average of this function than by just ...
-1
votes
1answer
41 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
0
votes
1answer
36 views

Average value of function that converges?

I have a function $f$ that converges to a value: $$ f(x) = 1−s−A \beta ^ x $$ Where $A \in \mathcal{R}$, and $0< \beta <1 $, $0< A <1 $ I want to get the average value of for $ x > ...
0
votes
1answer
27 views

Average of Numbers

Consider the following problem: if $a \leq b \leq c \leq d \leq e \leq f \leq 101$ and if average of these(a,b,c,d,e,f) numbers is 100 then what could be the least value of a?