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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7 views

Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: ...
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1answer
60 views

SAT Math Question Confusion

I was doing a practice new SAT Test and was wondering exactly what this question is asking and how it got to the answer. Thanks!
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1answer
18 views

Five-year Annual Average vs five-year Weighted average maintenance costs for two car types

If we are comparing maintenance costs (M$) per mile (M$/m = Mtype) of two car models over a 5 year period, where the number of cars that are type (a) is much less than type (b), and the number of type ...
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1answer
31 views

what does `ensemble average` mean?

I'm studying this paper and somewhere in the conclusion part is written: "Since this rotation of the coherency matrix is carried out based on the ensemble average of polarimetric scattering ...
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2answers
51 views

Weighted Average Distance between 3 or more points

I'm trying to find out the average point between 3 or more points, given each distance that the end point is away from each of the other points. With 2 points it's easy, I believe the formula should ...
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0answers
11 views

List of graph data points, need accurate calculation/estimate formula for excel

So I'm working on a small project that will use a calculation in excel, I'm nearly there and the only piece missing is being able to accurately estimate a data point from the following set of data ...
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0answers
9 views

“best fit” cisoid for N input cisoids

Suppose I have N cisoids -- each with its own amplitude, phase and frequency. Is there any sensible way to construct such a blackbox function that outputs a single cisoid that best represents the ...
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1answer
18 views

compute a value based on goegraphic range from measuement devices

Today is one of those days when the correct method to calculate this escapes me. I have 3 fixed points on a map where measurement devices are located. These all track the same transmitters. A mobile ...
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0answers
16 views

What kind of time series do I need?

I am trying to optimize a list of websites on which to purchase banner advertising using the following setup: For each banner ad impression I buy I am charged $0.001. When my ad is clicked it ...
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1answer
43 views

Average patients waiting time in dental office

At a Dental Office, patients come in at the rate of 20 per hour and, on average, are processed at the same rate. Patients wait in a queue till they are called up to the counter for registration. After ...
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0answers
22 views

Matlab, Extracting Particular Values from an Excel File

If I have a table of values in Matlab ( here I have a 40k rows, and about a dozen columns), how can I read only particular values from each row? My goal is to extract some of the values from each row, ...
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2answers
28 views

Explaining this inequality

In a proof I was working on today, I assumed this equation was true which lead to devastating results $$ \sqrt{\bar{x^2}} =\bar{\lvert x\rvert} $$ For instance, given the data 0 and 2, the left hand ...
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0answers
19 views

Averaging Models in Excel

I am working in Excel and have two sets of data points that come up with a percentage for the likelihood of a recession. I am wondering what the best strategy would be to combine these data points? ...
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1answer
23 views

The validity of dividing an average cost by an average duration?

Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative ...
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0answers
20 views

How do you calculate the weighting towards an average?

I guess in a way this is like calculating a weighted average, only backwards, i.e. from the average, we want to calculate the weightings Lets say there are two people A and B A's average call time ...
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0answers
58 views

How to calculate a weighted average over a closed surface ?

I'd like to understand a bit more the following problem. Suppose a potato shape (say a 3D volume bounded by a 2D surface), and define $n$ the normal vector to its surface, with components $n_i$. ...
2
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1answer
60 views

Average of elements in a subset of $\{1,2,3,..,n\}$ is greater than $\frac{n+1}{2}$ [closed]

Consider two integers $n \ge m \ge 4$ and $A=\{a_1,a_2,...,a_m\}$ a subset of the set $\{1,2,3,...,n\}$ with the property that $$\forall a,b \in A \text{ with } a \neq b, \text{ if } a+b \le n, \text{ ...
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1answer
6 views

Rate Times Distance Problem with Averages

On your drive to Hoover Dam, you maintain an average speed of 50 miles per hour on the way up. Returning home, you are only able to average 45 miles per hour because of heavy traffic. What is your ...
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1answer
38 views

What is the Difference in the Average and the Mathematical Expectation in the following Problem

Suppose that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students, for a total of 1000 students. The average class size is simply ...
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1answer
29 views

Adding up numbers * weights to get a result (not weighted average), does it have a meaning?

I have been comparing two solutions and used weights for individual areas based on their importance. I was interested which solution is better, i.e. which one has the higher score. The thing is I ...
3
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1answer
56 views

What is the maximum value of the sum $\sum_{i=1}^L(\bar{x}-x_i)$, in this specific case.

Let $x_i$ be a positive real variable, with $i=1,2,...,K$. We denote by $\bar{x}$ the average value of the values $x_1, x_2,...,x_K$. Let $a=\min_i x_i$ and $b=\max_i x_i$, then $x_i \in [a,b]$. My ...
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3answers
100 views

Is $\frac{a^2+b^2}{2}=c^2$ possible?

I am looking for an integer solution to the equation: $$\frac{a^2+b^2}{2}=c^2(a\neq b\neq c)$$ That is a square number that is the mean of two other square numbers, is this possible? And if so please ...
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1answer
29 views

How to find average of minimum value of two Poisson distributions?

I have two Poisson distributions with parameters $\lambda 1$ and $\lambda 2$. Now I want to find the average of minimum value of this two distributions. I mean that if I derive two random numbers ...
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1answer
89 views

Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
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0answers
29 views

Average Price Paradox

How can "owning 10 shares of ABC bought for average price of 2 per share" be an equivalent position to "owning 10 shares of ABC bought for average price of 6 per share"? Scenario A A1. Cash = 120, 0 ...
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0answers
52 views

How to find the average velocity of blood?

The velocity $v$ of blood that flows in a blood vessel with radius $R$ and length $L$ at a distance $r$ from the central axis is $$v(r) = \frac{P}{4\eta L}(R^2 − r^2)$$ where $P$ is the pressure ...
3
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0answers
38 views

Finding a summarizing vector for average angle calculation

Let $L$ and $R$ be two bags of positive vectors such that all vectors have length $k$. Define the distance $d_{avg}$ between the bags as the average pairwise angle between the vectors. Is is possible ...
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1answer
33 views

How to set up this algorithm?

I'm doing a simple budget app, to make some calculations to improve private economy. I've made an option where you can enter the value of the money that are in the bank right now, and how many days ...
16
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2answers
302 views

Geometric mean of prime gaps?

The arithmetic mean of prime gaps around $x$ is $\ln(x)$. What is the geometric mean of prime gaps around $x$ ? Does that strongly depend on the conjectures about the smallest and largest gap such as ...
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0answers
9 views

Properly average irregular samples into discrete regular ones

Imagine you have a device collecting data at not very regular time intervals. For plotting on graph or further processing, you'll want to turn the samples in regular ones, with constant time ...
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2answers
32 views

Infinite averages

If you wanted to find the average of infinite items, what would it be? Would an estimate of the first x averaged be a good estimate? Or would the value be nearly zero because you are dividing by ...
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2answers
46 views

Mean age among employees in a company.

In a company there are 32 men and 59 women. Male mean age is 48.5 and female 39.2. One of the women (47 years old) ended working at the company and was replaced with a 23 year old man. Calculate the ...
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1answer
58 views

Average distance between two random points in a square

A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square? For more general rectangle case, see here. The proof found there is ...
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1answer
50 views

Dropping the lowest number in a set lowers the mean average of the set.

So a friend of mine had her grade drop because her teacher had decided to drop the lowest grade. Is this possible or did the teacher mess up something? And if so, then how is it possible. We've ...
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2answers
48 views

Finding average using central limit theorem.

I'm have a lot of trouble trying to wrap my head around how exactly to use the central limit theorem in this question. Image a gambling casino consisting of 100 busy roulette tables. Suppose that ...
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1answer
36 views

Contraharmonic mean given harmonic mean

Given that two positive integers, $X$ and $Y$, have a harmonic mean of $6.875$, what is their contraharmonic mean. Harmonic mean is $(2XY)/(X+Y)$ and contraharmonic mean is $(X^2 +Y^2)/(X+Y)$. I began ...
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27 views

Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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1answer
22 views

Harmonic Mean equation/solutioin

Here is the question: A a number x is said to be the harmonic mean of y and z if 1/x is the average of 1/y and 1/z. a. Write an equation for which the solution is the harmonic mean of 30 and 45. b. ...
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1answer
48 views

What does $h$ and $x$ represent in $2x+h$

I was asked to find the average gradient between $x=2$ and $x=5$ on the curve $y=x^2+3$. My method: Average gradient = $\frac{f(x+h)-f(x)}{h}$ $$=\frac{x^2+2xh+h^2+3-(x^2+3)}{h}$$ ...
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1answer
28 views

Is the nth root of a product of n terms used in place of the average anywhere?

In applied usage we typically take the average of values or terms which is done by summing them and dividing by the number of terms (for simple average): $$\sum_{i=1}^n \frac{a_i}{n}$$ It dawned on ...
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1answer
38 views

Given any combination of the average of 5 of the 6 variables, find each of those 6 variables

Suppose that there are 6 variables: (a, b, c, d, e, f), and that some magic machine gives you the average of 5 of them any amount of times, so you can find the average of (a,b,c,d,e), or average of ...
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2answers
26 views

Is that possible to get all possible numbers, if I have only an average value, max, min number & also number of numbers?

I tried to find out the all numbers or set of possible combination of numbers. But I have only the averages value, maximum number, minimum number & also have tolal number of numbers. ...
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1answer
24 views

Prove that for all n exist order in which will not any average

Prove that for all $n \in \mathbb N $ from $1$ to $n$ exist order in which will not any average of two numbers. For example $2,3,5,1,4,6$ is incorrect because between $6$ and $2$ is their average $4$, ...
2
votes
2answers
72 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
34 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 ...
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1answer
27 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 ...
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1answer
31 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
19 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 ...
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0answers
27 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
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1answer
26 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 ...