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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math distribution of averages and distribution of standard deviation for comparison of bytes

Let me change my question: I have a sequence of 512 numbers (these 512 numbers can have a value between 0 and 255) (in computer mode these numbers can be between 00000000 and 11111111 (bits)). For ...
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APR Calculation

I'm hoping someone can clarify this for me. The model/example is this: We lend an amount of 1498.50 (loan amount). Other fees total 39.95. The term of the loan is for 12 months. There is no ...
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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?
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202 views

Power Mean Random Distribution

I'm trying to find a the distribution for the power mean of $n$ random variables on $[0,1]$. I've got the arithmetic mean: $\frac{n}{(n-1)!}\sum_{k=0}^{\lfloor ...
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26 views

Balancing merges of timed event

I'm making a game that can fuse few guns to create an equal gun and I need to compute the fused properties. First off I thought this was easy - I just took the inverse of the sum of the inverses of ...
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How do I calculate weighted mean with negative weights?

This might be very trivial for you guys. If : I buy 2 oranges for 5 dollars each then I buy 3 oranges for 6 dollars each and then I sell 3 oranges for 4 dollars each How do I calculate the average ...
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leading and lagging moving average indicator

What are leading short and lagging long moving average indicators and how do we calculate them? e.g. for the following data set, and let window size be 2. Can you ...
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156 views

I'm having trouble calculating ratings

I'm not a wiz at math and this problem has me a little stumped. I need the average score out of 5 but it's a little different how I do it. I have 5 fields, field one is rating one, field two is ...
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202 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 ...
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165 views

Basic question about natural density

Suppose that we have a sequence of finite sets $A_1, A_2, \ldots$, which partition $\mathbb{N}$. I am making no other assumptions on the $A_n$ - i.e. there could be any amount of interleaving between ...
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Proving correlation coefficient = 1 or -1 given X and Y=a + bX

Given $X$ and $Y = a+bX$, I have to prove that: If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$. I've gotten to the point where I have: $$ \rho = \frac{b \cdot \sigma_x }{ ...
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Find the average of a collection of points (in 2D space)

I'm a bit rusty on my math, so please forgive me if my terminology is wrong or I'm overlooking extending a simple formula to solve the problem. I have a collection of points in 2D space (x, y ...
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How to add and subtract values from an average?

Say I have 100 numbers that are averaged: number of values = 100 total sum of values = 2000 mean = 2000 / 100 => 20 If I want to add a value and find out the ...
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257 views

Bound on deviation between arithmetic and harmonic mean?

It is well known that, if HM denotes the harmonic mean and AM the arithmetic mean, we have $$ AM(x) \ge HM(x) $$ Now I am dealing with the expression $$ \frac{1}{HM(x)} - \frac{1}{AM(x)} $$ A ...
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What is to geometric mean as integration is to arithmetic mean?

The arithmetic mean of $y_i ... y_n$ 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 using ...
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Probability value in a skewed data

A question goes like this: Given that there 2 questions out of 3 questions to pass an exam and follow are details of number of people who attended the questions correctly, what is the maximum number ...
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612 views

Harmonic mean and logarithmic mean

The harmonic mean of a finite set of positive real numbers $\{x_1, x_2, \ldots, x_n\}$ is defined to be $$H(\{x_1, x_2, \ldots, x_n\}) = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + ...
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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 ...
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197 views

Average amount of money received from pulling three random coins

Let's say I have a bag of coins, which contains 1 quarter, 2 dimes, 3 nickles and 4 pennies. If I were to randomly pull out 3 coins, on average, how much money would I get?
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401 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 ...
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2answers
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Why is median age a better statistic than mean age?

If you look at Wolfram Alpha or this Wikipedia page List of countries by median age Clearly median seems to be the statistic of choice when it comes to ages. I am not able to explain to myself ...
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Is there a name (and use) for an average based on the unique values of a set of data?

Consider the following data points: $1, 1, 2, 3, 4$ I understand that... the average is the total of the numbers divided by the count of numbers in the set, the median is the central value based on ...
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How do I figure out what kind of distribution this is?

i've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram: Ping times have a minimum value, but a long upper tail. ...
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Which average to use? (RMS vs. AM vs. GM vs. HM)

The generalized mean (power mean) with exponent $p$ of $n$ numbers $x_1, x_2, \ldots, x_n$ is defined as $$ \bar x = \left(\frac{1}{n} \sum x_i^p\right)^{1/p}. $$ This is equivalent to the harmonic ...