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).

1629 questions
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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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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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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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Regular average calculated accumulatively

is it possible to calculate the regular average of a sequence of numbers when i dont know everything of the sequence, but just everytime i get a new number i know the total count of numbers and the average for the numbers - 1. for example: 2 3…
clamp
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Average in a rating between 1 and 5

A user can vote on these numbers: 1, 2, 3, 4, 5 Then it's displayed as groups like this: 1 - 5 votes 2 - 3 votes 3 - 1 vote 4 - 17 votes 5 - 2 votes Now I want the avarage rating score, like 3.9 or whatever it will be. What I tried and…
Jens Törnell
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Unorthodox way of getting the average of two numbers

I can't believe the alternative method I just saw to calculate the average of two numbers: I use the following: (a+b)/2 = avrg(a,b) (b+a)/2 = avrg(a,b) Found someone using this: a+((b-a)/2) = avrg(a,b) b+((a-b)/2) = avrg(a,b) How to calculate…
ajax333221
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Simple question regarding ratio and average

I have 2 lists of numbers (with an equal number of numbers in each). Each number is then divided by the number of which it is paired with (by index), and a ratio is received. I then want to calculate the global average ratio, so I try 2 ways: Sum…
Madara's Ghost
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Sum of averages vs average of sums

I have essentially a table of numbers -- a time series of measurements. Each row in the table has 5 values for the 5 different categories, and a sum row for the total of all categories. If I take the average of each column and sum the averages…
Daniel R Hicks
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Calculate average wind direction

What is the best way to average wind direction? I have found many conflicting suggestions elsewhere. Best one I saw is to average SINs of all angles in radians and take inverse SIN of the result. This is to be used to produce a windrose where the…
Kopernik
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What is the intuition behind the formula for the average?

Why is the average for $n$ numbers given by $(a+b+c+\cdots)/n$? I deduced the formula for the average of 2 numbers which was easy because its also the mid point, but I couldn't do it for more than 2 numbers.
Khalid T. Salem
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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 aggregates the info and generate a report every 2…
Guillermo
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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 T = 5, how would I add another value (let's say 10) and update the average correctly? Is this possible?
Jesse Brands
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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 mean, arithmetic mean, and root mean square for $p…
Sophie Alpert
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5 star ratings. Bayesian or Weighted average?

I am building a website which has 5 star ratings to rate items. These ratings unlike the normal ones are of unequal weights. i.e. 1 star: -5, 2 stars: 10, 3 stars: 20, 4 stars: 30, 5 stars: 50, Every time a user rates I am planning to calculate…
Cherian
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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?
LordZardeck
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