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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8
votes
1answer
382 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. ...
5
votes
4answers
4k views

What is the average of rolling two dice and only taking the value of the higher dice roll?

What is the average result of rolling two dice, and only taking the value of the higher dice roll? To make sure the situation I am asking about is clear, here is an example: I roll two dice and one ...
4
votes
1answer
134 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 $(...
44
votes
3answers
1k views

Expected number of people to not get shot?

Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle. At midnight, each gangster shoots the person that is ...
25
votes
11answers
4k views

Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.

I'm in an argument with someone who claims that a two mile in 7:59 does not imply that one mile (at some point within the two miles) was covered in under 4:00. This is obviously wrong, but I'm not ...
6
votes
4answers
3k views

How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
6
votes
1answer
6k views

5 star ratings. Bayesian or Weighted average?

I am building a website which has 5 star ratings to rate items. These ratings unlike the normal ones are of unequal weights. i.e. ...
4
votes
1answer
138 views

Dirichlet Series and Average Values of Certain Arithmetic Functions

If an arithmetic function $f(n)$ has Dirichlet series $\zeta(s) \prod_{i,j = 1} \frac{\zeta(a_i s)}{\zeta(b_j s)}$, for which values of $a_{i}$ and $b_{j}$ is the following true? That \begin{align} \...
7
votes
2answers
375 views

What does the $L^p$ norm tend to as $p\to 0$?

This is something I was thinking about, so I'm going to post it as a question and post my own answer. I hope that anyone who wants will comment, correct me if I'm wrong, and add their own knowledge ...
1
vote
2answers
149 views

Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
0
votes
1answer
239 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
votes
5answers
548 views

Is this a weighted average/percentage problem?

Let's say a Marketing company has a total turnover of 10000 \$ There are 3 salesmen A,B,C with the following turnovers A = 2000 $ B = 3000 $ C = 5000 $ Now, ...
28
votes
4answers
2k views

What is to geometric mean as integration is to arithmetic mean?

The arithmetic mean of $y_i \ldots y_n$ is: $$\frac{1}{n}\sum_{i=1}^n~y_i $$ For a smooth function $f(x)$, we can find the arithmetic mean of $f(x)$ from $x_0$ to $x_1$ by taking $n$ samples and ...
30
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 ...
6
votes
1answer
2k views

Regular average calculated accumulatively

is it possible to calculate the regular average of a sequence of numbers when i dont know everything of the sequence, but just everytime i get a new number i know the total count of numbers and the ...
4
votes
2answers
131 views

Average $lcm(a,b)$, $ 1\le a \le b \le n$, and asymptotic behavior

What is the average value for $\mathrm{lcm}(a,b)$, with $ 1\le a \le b \le n$, for a given $n$, and what is the asymptotic behavior? The $\mathrm{lcm}$ is the least common multiple. I have ...
7
votes
3answers
3k views

Average distance between two points in a circular disk

How can I find an average distance between two points lying inside a circular disk of a certain radius? I wonder if there is any other way except of using a Monte Carlo method?
4
votes
1answer
151 views

Mean value of the rotation angle is 126.5°

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 ...
4
votes
1answer
5k views

Average Distance Between Random Points in a Rectangle

My question is similar to this one but for rectangles instead of lines. Suppose I have a rectangle with sides of length $L_w$ and $L_h$. What is the average distance between two uniformly-distributed ...
2
votes
3answers
2k 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 ...
7
votes
3answers
295 views

Asymptotic difference between a function and its binomial average

The origin of this question is the identity $$\sum_{k=0}^n \binom{n}{k} H_k = 2^n \left(H_n - \sum_{k=1}^n \frac{1}{k 2^k}\right),$$ where $H_n$ is the $n$th harmonic number. Dividing by $2^n$, we ...
5
votes
1answer
356 views

Average sine of an angle between two rays in a cone

I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle. Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
3
votes
2answers
120 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
0
votes
1answer
287 views

Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency

Problem I'd appreciate some ideas on how to define a formula to estimate the value of a future data point for a continuously sampled event, based on past measurements and their tendency. At any ...
6
votes
4answers
147 views

Is there a way to get an average that weights each item inversely based on distance from the mean?

I'm not sure how to phrase this, or even if such a thing exists. Sorry! I have a bunch of data points, which are mostly pretty tight. Each group should hone in on a specific point in space. ...
3
votes
4answers
183 views

If $\sum\limits_{k=1}^n y_k\geq n$ and $\sum\limits_{k=1}^n \frac{1}{y_k}\geq n$, then $\prod\limits_{k=1}^n y_k\geq 1$?

Let $y_1,\ldots y_n$ be positive real numbers satisfying $y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$. Is it true that $y_1y_2\cdots y_n\geq 1$?
2
votes
1answer
147 views

Fréchet mean between points in $\mathbb{R}^3$

Let $X$ be a set of $n$ points in $\mathbb{R}^3$ and $f_m$ be the Fr├ęchet mean, i.e.: $$ f_m= \arg \min_{p \in M} \sum_{i=1}^n w_id^2(p,x_i) $$ where $(\mathbb{R}^3,d)$ is a complete metric space, $...
2
votes
1answer
62 views

Derivation of Running(Online) Variance's formula

I need to know the dimostration of Running Variance's formula: $$ \sigma_n^2 =\frac{(n-1)\sigma_{n-1}^{2}+(x_n-\overline{x}_{n-1})\cdot(x_n-\overline{x}_{n})}{n} $$
2
votes
1answer
355 views

Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
2
votes
3answers
1k 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?
1
vote
0answers
79 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 ...
1
vote
2answers
381 views

How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?

Let $a$, $b$, and $c$ be positive real numbers such that $a+b+c = 1$. Then how to establish the following inequality? $$ (1-a)(1-b)(1-c) \geq 8abc.$$ My effort: Since $a+b+c =1$, we can write $$ (...
1
vote
1answer
470 views

Calculating Average Time based on Success Probability

Interns of company XYZ has to pass 2 training programs in sequence. So Program 2 can only be taken after an intern has done Program 1. Each program has a success rate of 40% and each program takes 3 ...
1
vote
1answer
3k views

Use calculus to calculate the slope of a moving average line

I recently read a paper where it was stated that calculus was used to calculate the slope of a moving average line at a given point. Given that there is no real formula to differentiate with a moving ...
1
vote
2answers
67 views

Problem Solving using Algebra

If Peter is $7$ years older than Sharon and John is twice as old as Peter, work out how old Peter is if the average of their ages is $19$. Thanks! :)
1
vote
2answers
179 views

Probability of a normal random variable added to a number being greater than another normal random variable, and distribution of average

$X$= random height of a male $Y$= random height of a female $X$ and $Y$ are independent of each other For $x$, $\mu=180\text{ cm}$ and $\sigma^2= 16\text{ cm}^2$ For $y$, $\mu=170\text{ cm}$ and $\...
0
votes
1answer
986 views

Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
0
votes
1answer
71 views

Interesting Original Probability Question

I have 100 balls, which are all initially yellow. Every minute, I randomly choose a ball and paint it red. How many balls are expected to be red after 100 minutes? Note: I could pick up a ball that's ...
-1
votes
1answer
2k views

Can weighted average be used to calculate percentage increase? [duplicate]

Possible Duplicate: Is this a weighted average/percentage problem? Let's say a Marketing company has a total turnover of 10000 \$ There are 3 salesmen A,B,C with the following turnovers: The ...