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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3answers
119 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) ...
2
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3answers
294 views

Erased number?

A set of consecutive positive integers starting with 1 is written on the board. A student came along and erased one number. Average of remaining numbers is 61 15/20 . What was the number erased
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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 ...
2
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3answers
763 views

Averaging the values of $\cos x$ over one period

I'm calculating the average value of $\cos x$ by dividing the period $[0,2\pi]$ into ten intervals which means that I should be looking for the average of 11 results. What I get is approx. 0.09. The ...
2
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3answers
82 views

Why should ${\sum_1^n {s_i} \over \sum_1^n {t_i}} = {n \over \sum_1^n{t_i \over s_i}}$? (harmonic mean)

I realized it reading about computer performance. This identity is presented there with words: dividing total distance by total time, you arrive at average execution rate on the left. On the right, ...
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2answers
10k views

Is the average of the averages equal to the average of all the numbers originally averaged?

I am tempted to say yes because of the following pseudo-proof (I say pseudo-proof because I am not convinced): $$ \frac{\frac{w+x}{2}+\frac{y+z}{2}}{2}=\frac{w+x}{4}+\frac{y+z}{4}=\frac{w+x+y+z}{4} ...
2
votes
1answer
410 views

Need help with a math trick question

I wasnt sure where to ask this but since this is an algorithmic question here it goes. I've come face to face with a math problem and can't seem to get over it for the last couple of days. It goes ...
2
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2answers
44 views

A Percentage of Averages

A company brags about the speed of their service, "75% of our assignments are completed in an average of 20 days." Is this a meaningful claim? Or is it kind of like saying, "60% of the time, it ...
2
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2answers
86 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 ...
2
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3answers
121 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 ...
2
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1answer
63 views

What is this physics simulation formula doing?

I have encountered a piece of code that performs a physics simulation of a moving projectile. I'm trying to understand what the mathematical basis is for a bit that looks like this: $$ d_1 = f(x) $$ ...
2
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2answers
141 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 ...
2
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2answers
21k views

What is the difference between the normal average and weighted average?

What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and also,how to get the weighted average of some ...
2
votes
2answers
151 views

Calculating statistic for multiple runs

I have s imple, general question regarding calculating statistic for N runs of the same experiment. Suppose I would like to calculate mean of values returned by some Test. Each run of the test ...
2
votes
2answers
2k views

Finding percentile rank without knowledge of distribution

Say you take a test and are told your individual score, as a percentage. Eg: 95%. You are also told the aggregate score (average) of all students together, as well as how many students in total took ...
2
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4answers
802 views

Get `n` random values between 2 numbers having average `x`

I want to get n random numbers(e.g n=16)(whole numbers) between 1 to 5(including both) so that average is x. x can be any value between (1, 1.5, 2, 2.5, 3, 3.5, 4, ...
2
votes
2answers
418 views

Probability cut-off

Is there a probability cut-off point? e.g. if the probability of something keeps halving do you stop at a certain point and say the rest of the possibilities are negligible? What do you do then? ...
2
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2answers
4k views

What is the standard error of the mean of an exponential distribution of the form $Ae^{Bx}$ with N measurements?

What is the standard error of the mean of an exponential distribution of the form $Ae^{Bx}$ with $N$ measurements?
2
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2answers
35 views

Is there a name for the way I am averaging the cost of cards?

My buddy and I were discussing different ways of deciding how much mana to include when constructing a deck. Without thinking much about it I used a method of finding the average converted mana cost ...
2
votes
1answer
39 views

Is not always the accumulated probability until the expected value equal to 1/2?

My problem is that doing calculations with exponential distribution, the result I get is not 1/2, and I think it should be that according to the intuitive concept of the expected value. The density ...
2
votes
1answer
76 views

Why is the average of a sum equal the sum of the averages?

I came across this website showing the proof of the above question in the Expected Value section. However, I do not quite understand why the probability of $xy$ becomes the probability of $x$ (or $y$) ...
2
votes
1answer
581 views

How to calculate new mean if population is unknown?

I have three values Mean (population mean, not from sample) $\bar{x} = 3$ Number of elements in population (number of values in original set) $n = 15$ A new value $x_{(n+1)} = 7$ What is ...
2
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1answer
281 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
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1answer
324 views

Geometric Mean of an Interval

Is there any way to calculate one? If it't not clear what I mean, here's an example: Starting with an initial value, keep multiplying it by some random amount on the interval [1, 2] at regular ...
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4answers
1k views

Finding mean of $n$ consecutive numbers using a shortcut

I am working on the following question: Let us say we have $n$ consecutive numbers labelled $x_1$ to $x_n$. I want to find the average of these. The quickest way to do this seems to be ...
2
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3answers
2k views

from weighted average to single values

think about when you're computing a weighted average: you do something like W = sum(amount*weight) / sum(weight) Now I need to find every amount (amount0, amount1.....) starting from knowing the ...
2
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2answers
925 views

How do I average out to a particular number if I have to add another number to get that average?

So, lets say, that you have the following numbers (4, 15, 3, 22) and you have to add the fifth number (which I would call X) and they must average out to say 20. What do you have to do? I figured ...
2
votes
2answers
75 views

How do I find the average of top list items? [closed]

Here's the situation: I have a lot of "top lists" like so: list1: iPhone 6 Galaxy S5 LG G4 list2: Galaxy S5 OnePlus One iPhone 6 LG G4 Nexus 5 list3: LG G4 Galaxy S5 Nexus 5 And so on... ...
2
votes
1answer
22 views

Extrapolate data points from a series of averages

Given a series of data points: $$\begin{array}{c|c|c|c|c|c|c|c|} & \text{Monday} & \text{Tuesday} & \text{Wednesday} & \text{Thursday} & \text{Friday} & \text{Saturday} ...
2
votes
1answer
75 views

Average of a list of numbers, read one at a time

I have a dilemma Lets take the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ If we wanted to calculate the average of this set we would add up all the numbers in the set $(45)$ and then divide by the total ...
2
votes
2answers
105 views

weighing avg by columns vs rows outputs different results

First of all, I just know the basics of math, so please be patient. I have an overall score for a company with the product1 and product2. However when I do the overall for each criteria like ...
2
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1answer
85 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{ ...
2
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2answers
67 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 ...
2
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2answers
855 views

Adding to an average without unknown total sum

Let's say I know the following: Let A be the average value Let T be the number of values Assuming that A = 4.3 and ...
2
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1answer
197 views

Time to extinction

Suppose that a population has a rate of extinction equal to $k \exp({-\epsilon N})$ where $\epsilon$ and $k$ are constant and $N$ is the population size. This also means that the time to extinction is ...
2
votes
1answer
61 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
1k 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 ...
2
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1answer
97 views

Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
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?
2
votes
2answers
300 views

Least Squares Fit

So here's the question: Given a collection of points $(x_1,y_1), (x_2,y_2),\ldots,(x_n,y_n)$, let $x=(x_1,x_2,\ldots,x_n)^T$, $y=(y_1,y_2,\ldots,y_n)^T$, $\bar{x}=\frac{1}{n} ...
2
votes
1answer
3k views

Weighted average vs. weighted mean

Is there a formal difference between weighted average and weighted mean? I get corrected to the latter if I type in the former in wikipedia, and then there is a lot of stuff about the name "average" ...
2
votes
1answer
111 views

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$?

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$ ? It may seem this way but how can we show that indeed it is $\frac{1}{2}$. We know that the ...
2
votes
1answer
135 views

What is the best way to average the frequency of Chinese characters in a sentence?

I'm trying to find the best way to assign a "frequency score" to sentences in Chinese. Basically, I have a database which tells me how frequent each Chinese character is. From that, I would like to ...
2
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1answer
131 views

How are Tr(AB) results restricted?

In quantum mechanics one postulates that for each state $i$ there is a matrix $A_i$ and for each measureable dynamical variable $j$ (velocity etc.) there is a matrix $B_j$. Both are Hermitian matrices ...
2
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2answers
213 views

How can I show this in a summation?

I am trying to work out a summation for packet delays which is very similar to the summation for estimating RTT, which is an exponentially weighted moving average. I have modified the estimating RTT ...
2
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1answer
31 views

Two player game about maximizing earnings subject to an interesting condition

Me and my friend had a bet. We each pick an integer between $1$ and $100$ inclusive and reveal it at the same time. Whoever picks the higher number has his number halved. Then the person whose number ...
2
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2answers
47 views

Estimated wait time for a library book

A library has 20 copies of a book that circulates for 3 weeks. All copies are out and there 40 people on reserve ahead of me. How do I estimate the wait time?
2
votes
1answer
142 views

Average question GRE

The average daily temperature from 9th to 16th January(both inclusive) was 38.6 C and that from the 10th to 17th January(inclusive) was 39.2 C. what was the temperature on 17th January? I am able ...
2
votes
1answer
35 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
2
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1answer
31 views

Choosing two sets of values with the least difference between the averages of the sets

This is probably a simple Combination problem but I can't think of how to solve it in LibreOffice. I run multiplayer games along with seven of my friends, on two teams of 4 players each, for a total ...