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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22
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
1k 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 ...
4
votes
1answer
3k 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. ...
3
votes
2answers
947 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 ...
7
votes
2answers
142 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
109 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
5answers
370 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
2answers
1k 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 ...
4
votes
1answer
549 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 ...
7
votes
3answers
261 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
144 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. ...
6
votes
4answers
109 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
1answer
258 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
4answers
176 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
139 views

Average number of rolls of die to see each side at least once [duplicate]

Possible Duplicate: A Question About Dice You have a weighted n-sided die. Every side of the die is weighted differently where side n1 has a weight of w1, n2 has a weight of w2, ... ...
2
votes
1answer
112 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
205 views

Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
1
vote
2answers
51 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
votes
1answer
1k 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: ...