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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2answers
30 views

Five members of a wrestling team are weighed and …

An average weight is calculated after each player is weighed. Of the average weight increases by 2 pounds after each player is weighed, how much is the last player than the first? My answer is 8 ...
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1answer
192 views

Average value of a piecewise defined function

Consider the function $f$ defined by $$ f(x) = \begin{cases} x, & 0 \leq x < 1 \\ x^2, & 1 \leq x < 2 \\ \vdots \\ x^n, & n-1 \leq x < n. \end{cases} $$ I'm trying to compute ...
1
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0answers
50 views

Finding possible numbers to yield a certain arithmetic mean (average)

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that: the arithmetic mean will be calculated from 20 integer numbers, each having a ...
2
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1answer
37 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
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1answer
42 views

Are the $L^p$ norms ordered by $p$?

A question left over from this post is: Are the $L^p$ norms ordered by $p$ like the power means are?
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1answer
65 views

Catastrophic Cancellation

I need some informations about algorithms to solve the problem of Catastrophic Cancellation, or in general to calculate mean and variance of a data stream. For example about Donald Knuth's algorithm ...
0
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0answers
13 views

Averages of sets adding to a constant

... Wow, I really need to learn how to make titles that make sense... I have a group of users each submitting a set of numbers. This set of numbers always totals $S$. The overall set looks something ...
6
votes
2answers
147 views

Intuition on why the average minimizes the euclidean distance

I saw that there was a question with a very similar (if not identical) flavour to my question, but the answer was derived from derivative, the method that I already knew solved this problem. I feel ...
2
votes
1answer
67 views

Maximum and minimum of weighted sum

For $w_i\ge 0$ and some constants $\alpha_i , i=1,...,n$, what is the maximum and minimum of $\sum_{i=1}^{n}\alpha_i w_i$ subjected to $\sum_{i=1}^{n}w_i=1$? Intuitively, I put all weight on the ...
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2answers
115 views

Average number of people required to find a pair with same birthday

I have to find the expected number of people required to find a pair with same birthday. This is what I tried: Assume that there are $M$ possible birthdays, then following the definition for expected ...
6
votes
1answer
112 views

How to compute the mean average exponent of the naturals? What is the limit for large numbers?

With a friend I was trying to get an understanding for why the expected gap between primes is logarithmic. With that motivation I tried to express the average exponent of numbers. By average ...
2
votes
1answer
177 views

Is there a scientific way to assign weights to historical data?

This is a common question I usually face while processing historical data. I have year on year data of an event for the past N years.I would like to assign weights to the data of these N years so that ...
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1answer
69 views

Average percentage formula

I have something like: Price Quantity Tax (%) 2.2 34 8 1.3 29 7 And so on... After that I get something like: ...
2
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0answers
71 views

Have averages, need variance

I have a large spreadsheet, generated by a colleague, that contains the results of $E$ experiments. For each experiment, he calculated the average of $M$ measurements. I need the calculate the ...
0
votes
2answers
46 views

Get N values between 0 and 1 AND control spacing of results.

So I need to get N number of values between 0 and 1. The values should be evenly spaced. Thats easy... However, I also want another variable X that will shift the resulting values closer to 0 or 1. ...
0
votes
1answer
60 views

Most accurate mean for grouped/ranged data

I've got data in a range and frequency format e.g 0-5 : 3, 6-10 : 70 etc up to 31-35. How do I get the most accurate mean for such data?
0
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0answers
25 views

Getting the average of a serie of values

I am trying to smooth out a serie of values that represents tempo values, depicted in blue. The data comes from a tempo detection algorithm that as you might have guessed is not the best in town, the ...
2
votes
2answers
85 views

Averages in series

I have a series of numbers: $1,2,3$ I'm calculating a simple average between, them $(2)$. Now, I'm deleting the series and have no information regarding how many elements there were in the series or ...
0
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1answer
42 views

Proper Weighted Average

If I have a 3x3 matrix of information where the row totals describe the total goods produced by a particular company and the column totals provide the total for a particular type of good for all ...
1
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1answer
185 views

CAGR, log of negative numbers

I am trying to calculate the Compound Annual Growth Rate (CAGR) of a number of companies using the Geometric mean of the annual growth of their EPS. Some of the EPS values are negative(loss making) ...
2
votes
3answers
98 views

Average of the smaller of three random numbers from $0$ to $1$

A friend of mine claims he saw the following question on a math puzzle site:- What is the average of the smaller of three random numbers from $0$ to $1$? And they've given these options:- $A) ...
0
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2answers
46 views

Simple integral related to average value of a function

Prove that $\displaystyle \int_0^{\frac{\pi}{2}} \sin^2 x\ dx = \int_0^{\frac{\pi}{2}} \cos^2 x\ dx$ by making the change of variable $x = \frac{1}{2}\pi - t$ in one of the integrals. This problem ...
2
votes
2answers
55 views

Rate of appearance of digits 7 and 8 in a given sequence

This is from Arnold's Mathematical Methods of Classical Mechanics: let us consider the sequence $$ 1,\ 2,\ 4,\ 8,\ 1,\ 3,\ 6,\ 1,\ 2,\ 5,\ 1,\ 2\ \ldots $$ which consists of the first digits of the ...
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1answer
44 views

Properties of weighted average ratio of weights

Suppose we have two sets of weights $w_i$ and $u_i$; i.e., $\sum w_i =\sum u_i = 1$, and $0 \le w_i \le 1$, $0 \le u_i \le 1$. Consider the weighted average ratio R of these weights: $R \equiv \sum ...
5
votes
7answers
783 views

3 trams are coming every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come?

3 trams are coming to the stop every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come? It's a practical problem, not some kind of a riddle for which I have a ...
1
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1answer
42 views

What is the name of this “generalized sum”?

I'm looking for the name of this quite basic function: $X=\sqrt[\alpha]{\sum_i{x_i^\alpha}}$ ($\alpha\in\mathbb R$) It's a kind of "generalized sum": $\alpha=1$ : $X=\sum_i{x_i}$ $\alpha\to\infty$ ...
0
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1answer
104 views

Weighted mean from a set of average and standard deviation pairs

I'm trying to replicate some math a professor did related to Twitter sentiment analysis. Basically, there is a sentiment dictionary, called ANEW, that contains a mean and standard deviation for 3 ...
1
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0answers
72 views

Deal or No Deal: Arithmetic, Median or Geomtric mean?

I'm trying to decide which type of mean is best to use when playing Deal or No Deal (in terms of comparing it with the Banker's offer). I realise the standard answer would be the arithmetic mean, but ...
5
votes
4answers
159 views

$x$ is equal to at least $51$ of $a_1,\frac{a_1+a_2}{2},\ldots,\frac{a_1+a_2+\ldots+a_{100}}{100}$. Prove that $2$ of $a_1,\ldots,a_{100}$ are equal.

If $x$ is equal to at least $51$ number of the array $a_1, \frac{a_1+a_2}{2},\ldots,\frac{a_1+a_2+\ldots+a_{100}}{100}$, prove that $2$ numbers of the array $a_1,a_2\ldots,a_{100}$ are equal. ...
0
votes
2answers
35 views

What formula would you use to cast an average of several numbers into a smaller range?

Say I have four numbers ranging in value from 15-95. If I want to, for a simple example, say that if the average of the four numbers is 15 (lowest possible value), that would relate to 2 on a scale of ...
-1
votes
3answers
470 views

formula for converting a very long number to a fraction

What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2? the answer is $4\frac{6}{7}$. The sum of numbers is 34 and when you divide by 7 it's 4.8571428..... How can I get the fraction of ...
1
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1answer
68 views

Prove inequality of generalized means

Consider the generalized (power) mean of positive numbers $a_1, \dotsc, a_n$ $$M_p(a_1, \dotsc, a_n)=\left(\frac{a_1^p + \dotsb + a_n^p}{n}\right)^{1/p}\qquad p\in \mathbb{R}$$ where for $p=0$ we use ...
2
votes
3answers
68 views

Correct way to get average price

probably a basic question for a lot of you guys, but it was a subject of a friendly debate at my work earlier - needless to say none of the involved were accountants. In short, we are thinking about ...
7
votes
2answers
203 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 ...
0
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3answers
98 views

Should you average or add together daily bank balanace averages?

I work in the finance field and I am looking at average balances on bank statements balances. When I have more than 1 bank statement I need to reflect the overall average balance between the ...
1
vote
1answer
191 views

Sum of weighted squared distances is minimized by the weighted average?

Let $x_1, \ldots, x_n \in \mathbb{R}^d$ denote $n$ points in $d$-dimensional Euclidean space, and $w_1, \ldots, w_n \in \mathbb{R}_{\geq 0}$ any non-negative weights. In some paper I came across the ...
5
votes
6answers
1k views

Confusion with the definition of mean value

For some reason the formula for mean started to trouble me: $$\mu = \frac{1}{b-a}\int_a^b f(x)\:dx$$ The reason this confuses me a bit is because when I read this formula I read it as: ...
0
votes
0answers
100 views

Calculate the value based on the number of people who assess the sheep.

I explain my situation. I have 30 sheep producing milk and 10 different customers that assess drinking it. To determine which of sheep milk is the best I would like to figure out how to establish a ...
2
votes
1answer
125 views

Rating System: Statistically significant with weighted entries

The title may be a bit confusing because I not exactly sure how to do/explain what I am after. I have judges rating an object on a score 1-100, where the majority of objects will in the range 85-95 ...
3
votes
1answer
26 views

Simplified Averages - Always true?

While working on an "average rating" function for a website, I came across an idea for simplified averages, but I want to confirm that it always works. If it does, I might be able to keep a running ...
1
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2answers
370 views

Working out a percentage of from values

Using the following numbers as an example: 293.21 478.93 485.44 544.78 569.48 593.82 I know how work out the average (mean) value: ...
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votes
1answer
67 views

Moving averages and crossovers in stock markets?

Suppose I take a two moving averages to analyse stock market prices - one $200$ day moving average, $m_{200}$, and another $50$ day moving average, $m_{50}$. How do you decide when to sell and when ...
1
vote
1answer
46 views

is this or (when) does this equality hold for weighted power series

$s_n=\sum _{k=0}^n a_k$ for every $n$ and $x\in(0,1)$. Let $p=(p_n)$ is a sequence of nonnegative numbers with $p_0>0$ s.t $P_n= \sum_{k=0}^{n}p_k \rightarrow \infty$ as $n \rightarrow \infty$ ...
1
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0answers
22 views

Estimator of Absolute Error?

Given $X \sim B(n, p)$, we know that $\hat{p} = X / n$ is the obvious estimator for unknown parameter $p$, and the following quantity $$\frac{\hat{p}(1-\hat{p})}{n-1}$$ has the property that its ...
0
votes
2answers
84 views

Algorithm for finding lowest average grade difference

Given a class with n boys and n girls, in which the girls recieved the grades P1,...,Pn, and the boys recieved the grades S1,...,Sn in an exam, find a pairing of girl-boy in a way that minimizes the ...
1
vote
1answer
44 views

Difference between $\sum_{i=1}^{k}{\frac{s_i}{kn_i}}$ and $\frac{\sum_{i=1}^{k}{s_i}}{\sum_{i=1}^{k}{n_i}}$

I am getting confused at how to calculate the average probability. Suppose we repeat a kind of binary survey $k$ times each of which was done on a completely separate sample group. For each $i^{th}$ ...
0
votes
1answer
26 views

Normal Distribution with Regards to Time and Percentages

The length of time for students to complete a test is found to be normally distributed with mean 70 minutes and standard deviation 12 minutes. How long should the time for the test be if we wish for ...
3
votes
1answer
402 views

The Exponential decay.

I am studying semiconductor physics. there is a paragraph about Drude model in E.spenke's book "Electronic semiconductors" page 259 in art §9: "if on the average, a time $τ$ elapses between two ...
1
vote
1answer
92 views

Help with my math problem, New Average with a number deleted

A set of consecutive integers were written down: $1, 2, 3, 4, 5, ... x-1, x, x+1, ... n-2, n-1, n$ One number, $x$, is deleted. The arithmetic mean of the remaining numbers is $602/17$. What does ...
0
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1answer
216 views

find the average of a student [closed]

Five students in a closed room want to find average of their exam scores without revealing their personal score to each other. How can they do it? Hint: they can write something on paper and pass it, ...