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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1answer
18 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 ...
0
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0answers
13 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 ...
0
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0answers
57 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
54 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{ ...
0
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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 ...
0
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1answer
34 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 ...
1
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1answer
14 views

What is the best method to calculate the mean for sales of a product over a period of time? [closed]

I'm calculating the average sales over a period of N days of a product to project when a stock out might occur. The most basic method, summing all the sales for each day and dividing by the number of ...
0
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0answers
8 views

Please help me with this problem related to average weekly sales

A company determines that its weekly online sales, S(t) , in hundreds of dollars, t weeks after online sales began can be estimated by S(t)=73e^ t . Find the average weekly sales for the first 2 weeks ...
-1
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2answers
28 views

Find average speed, given speeds of two legs [closed]

A train runs for $3$ hours at speed of $55~\text{km}/\text{hour}$, for the next $2$ hours it runs at $65~\text{km}/\text{hour}$. Find the average speed of the train for a $5$ hour journey?
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1answer
13 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
votes
1answer
54 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 ...
1
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3answers
96 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 ...
1
vote
1answer
24 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 ...
0
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1answer
68 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 ...
0
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0answers
27 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 ...
0
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0answers
44 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
26 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 ...
1
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1answer
30 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
270 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 ...
0
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0answers
8 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 ...
1
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2answers
29 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 ...
1
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2answers
42 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 ...
1
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1answer
45 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 ...
-2
votes
1answer
44 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 ...
0
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2answers
42 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 ...
0
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1answer
34 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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0answers
25 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 ...
0
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1answer
19 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. ...
0
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1answer
40 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 = $\frac{f(x+h)-f(x)}{h}$ $$=\frac{x^2+2xh+h^2+3-(x^2+3)}{h}$$ ...
1
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1answer
25 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 ...
0
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1answer
31 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 ...
1
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2answers
22 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. ...
0
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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
65 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 ...
0
votes
1answer
26 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
30 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
13 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
19 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
22 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
26 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
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1answer
12 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
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0answers
17 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 ...
4
votes
3answers
48 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
61 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
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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
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1answer
57 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
50 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
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1answer
15 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 ...