Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [average]

Averages summarise a set of values in one way or another. Without further qualification it most commonly refers to the arithmetic mean, but other averages such as root-mean-square exist.

In its most general definition, an average is a summary of a set of values. Normally it refers to the arithmetic mean, but other means may be employed (geometric, harmonic, etc.) or a transformation may be applied before and after taking a mean (e.g. root-mean-square).

1651 questions
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Incremental averaging

Is there a way to incrementally calculate (or estimate) the average of a vector (a set of numbers) without knowing their count in advance? For example you have a = [4 6 3 9 4 12 4 18] and you want to get an estimate of the average but you don't…
Ali
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Why is an average of an average usually incorrect?

Can someone explain why taking an average of an average usually results in a wrong answer? Is there ever a case where the average of the average can be used correctly? As an example, let's say that an assessment is given to three schools and I…
O.O
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The math behind Warren Buffett's famous rule – never lose money

This is a question about a mathematical concept, but I think I will be able to ask the question better with a little bit of background first. Warren Buffett famously provided 2 rules to investing: Rule No. 1: Never lose money. Rule No. 2: Never…
The Gilbert Arenas Dagger
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What is the arithmetic mean of no numbers?

I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the arithmetic mean and how many numbers were given. However, when you don't give them any numbers, one says the arithmetic mean is…
Ky -
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What is the difference between Average and Expected value?

Question : What is the difference between Average and Expected value? I have been going through the definition of expected value on Wikipedia beneath all that jargon it seems that the expected value of a distribution is the average value of the…
user2340452
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Expected number of people to not get shot?

Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle. At midnight, each gangster shoots the person that is nearest to him. (A person can get shot more than…
John Smith
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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 new average: total sum of values = 2000 + 100 mean = 2100 / 101 => 20.79 If I want to…
Zabba
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Do I have a misconception about probability?

I have come across this text recently. I was confused, asked a friend, she was also not certain. Can you explain please? What author is talking about here? I don't understand. Is the problem with the phrase "on average"? Innumerable…
Lukasz Skowron
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What is to geometric mean as integration is to arithmetic mean?

The arithmetic mean of $y_i \ldots y_n$ 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 the above formula. As $n$ tends to infinity, it…
netvope
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Pascal gets drunk and builds his triangle. Half the time he writes $0$ instead of adding the two numbers above. What is the average of the numbers?

One day Pascal has a little too much to drink, then sits down to build his famous triangle. He writes $1$'s going down the sides, no problem. Then he starts the arduous task of filling in the triangle. Each number is supposed to be the sum of the…
Dan
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What is the mean value of $|\sin x +\sin (\pi x)|$?

I was thinking about non-periodic trigonometric functions, and came up with this question: What is the mean value of $|\sin x +\sin (\pi x)|$ ? Here is the graph of $y=|\sin x +\sin (\pi x)|$: The mean value should be $\lim\limits_{n\to\infty}…
Dan
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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 zero to set the average. But you can make a similar…
user85543
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What is the difference between statistical mean and calculus mean?

For example in statistics we learn that mean = E(x) of a function which is defined as $$\mu = \int_a^b xf(x) \,dx$$ however in calculus we learn that $$\mu = \frac {1}{b-a}\int_a^b f(x) \,dx $$ What is the difference between the means in…
Johnathon
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what does `ensemble average` mean?

I'm studying this paper and somewhere in the conclusion part is written: "Since this rotation of the coherency matrix is carried out based on the ensemble average of polarimetric scattering characteristics in a selected imaging window, we obtain…
Sepideh Abadpour
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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 sure how to create a proof showing otherwise. Does…
Nick
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