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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7 views

Zonal averaging of partial derivatives

Given a quantity $Q(x,y,t)$, the zonal average operator $[Q] = \frac{1}{2\pi}\int_0^{2\pi} Q\:\mathrm{d} \lambda$, and zonal anomaly $Q^\star$ such that $Q = [Q] + Q^\star$, my text book says that ...
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15 views

Find spikes in data

I have some datasets and I need to find spikes in them. Imagine the data looks like trading data. If the spike is big enough, I need to log it, otherwise, proceed in the analysis. I tried with a ...
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1answer
36 views

Calculating the average of multiples and divisions

Imagine a number line that contains every value that is greater then (but not inclusive of) 0. The center of the line is 1. On the right side of the center(1), obviously, are all the whole and ...
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1answer
16 views

What statistical equation am I looking for?

Suppose you have two data sets: Dataset A: 4,2,6,5,3,3,5,4,4 Dataset B: 8,0,0,8,9,1,1,9,0 Both data sets have a mean of 4, but dataset A's values center much more around the mean whereas dataset ...
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1answer
29 views

Why must average only be used with normal distribution?

In a technical job interview I was asked a question that I couldn't quite make sense of. The interviewer was talking about sampling a sound file to make a visual effect (such as a graph that moved to ...
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1answer
19 views

A Basic Math Question on Averages

Okay this is going to sound really stupid but I'll ask anyway... I need to get a $5.5$ accumulative GPA (the highest is a $7.0$). For the last $16$ classes I've done my GPA is sitting at $5.44$. I'm ...
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1answer
18 views

Running a Cumulative Average

I'd like to run a cumulative average and I'm wondering if my process is sound. Here's a small dataset: Row 1: $\frac{2\cdot 60}{58} = 2.07$ Row 2: $\frac{4\cdot 45}{44} = 4.09$, ...
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62 views

How to prove the integral function with cosine is increasing

Prove that the following function is an increasing function on $x\in (0,1)$ when $n\ge2$. $f(x) = \int_0^{\pi} \frac{1}{(1-2x\cos\theta+x^2)^n} d\theta$
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1answer
25 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 $v_1, ..., v_n$, ...
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1answer
26 views

weighted average with exponential weighting

I want to create weighted average, where weights depend on value of number. If I want exponential weights is this regular? $average = \log_e(\frac{\sum_{i=1}^n e^{v_i}}{n})$ Isn't it just average of ...
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1answer
27 views

What kind of a mean value is this?

I wasn't that sure what kind of mean value the following is, I hope you can help me out: What it's about: I have this testseries of about 30 elements, that delay the boot sequence of an embedded ...
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1answer
18 views

Count if there are more smaller or larger number in a result made of multiple Xs?

Firstly, I am not a math pro or something. So far I was able to use math for my needs, but now I am at my wits' ends. Here is the deal. These things are known to me: ...
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2answers
23 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
34 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 ...
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0answers
28 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
30 views

Derivation of Running(Online) Variance's formula

I need to know the dimostration of Running Variance's formula: $$ \sigma_n^2 =\frac{(n-1)\sigma_{n-1}^{2}+(x_n-\overline{x}_{n-1})\cdot(x_n-\overline{x}_{n})}{n} $$
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1answer
36 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
45 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 ...
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0answers
8 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 ...
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2answers
52 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
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1answer
34 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
92 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 ...
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1answer
90 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
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1answer
51 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
32 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: ...
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0answers
64 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 ...
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2answers
29 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. ...
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1answer
17 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?
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0answers
17 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
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2answers
77 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
32 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 ...
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1answer
31 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) ...
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3answers
63 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) ...
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2answers
36 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 ...
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2answers
51 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
25 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 ...
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7answers
326 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 ...
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1answer
33 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": $\alpha=1$ : $X=\sum_i{x_i}$ $\alpha\to\infty$ ...
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1answer
46 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 ...
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0answers
40 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
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4answers
149 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. ...
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2answers
28 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 ...
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3answers
50 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 ...
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1answer
34 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 ...
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3answers
47 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 ...
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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 ...
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3answers
75 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 ...
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1answer
54 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 ...
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6answers
411 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: ...
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0answers
91 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 ...