Mathematics Stack Exchange
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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).

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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 location in the set, the mode is the value…
Philip Regan
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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 numbers?Also,do we have first to get the mean(normal…
Firework32
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Is there a way to get an average that weights each item inversely based on distance from the mean?

I'm not sure how to phrase this, or even if such a thing exists. Sorry! I have a bunch of data points, which are mostly pretty tight. Each group should hone in on a specific point in space. Unfortunately, some of the recordings are polluted with…
Tom Wright
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Geometric Mean of a Function

If the $(\int_a ^b f(x))/(a-b)$ is the arithmetic average of all the values of $f(x)$ between $a$ and $b$, what is the expression representing the geometric average of all these values?
William Grannis
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what is the argument for not using the average of an average?

I want to disprove someone's calculation of percentage of cash sales for a year by taking summing percentage of cash sales by month and dividing by 12. I sense the correct way is to take total cash sales for the year and divide by total sales for…
denise
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average of four numbers, zero sum?

I am not sure if this is the case for just four numbers, but here is my question if someone could verify. If you take the mean of four numbers, subtract the mean from each of the four numbers, and then take the sum of these differences, is the sum…
Emily O.
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Prove that if 2000 m is run in 4:50, then one mile is run under 4:00

Prove that if 2000 m is run in 4:50, then one continuous mile is run under 4:00. I was thinking -- yeah, this follows easily from the other question, where I asked that if 2 miles are run in 7:59, then one mile must be run under 4:00. But then I…
Nick
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Sum of averages to averages of sum

I have the following values $\overline{b}$, and $\overline{u}$ which is : $\overline{b} = \dfrac{b_1+b_2+b_3+b_4}{7}$, $\overline{u} = \dfrac{u_1+u_2+u_3+u_4}{7}$ is there any way I can get the following if I have only value of $\overline{b},…
Gaurav Shah
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How do I average a new number into an established percentage if I know the number of items?

This seems like something I should be able to do but I can not for the life of me figure it out. I'm writing a program to calculate an average score; let's say that my data looks like this. x = number of votes y = current rating z = new rating Is…
Andrew Klatzke
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What is the name of this type of "average"?

Given two variables $x$ and $y$, $$\frac{2}{1/x + 1/y} $$ looks like some kind of average of $x$ and $y$. Is there a name for it? Where can i look up more information (such as properties) of this type of average?
Tim
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Real world examples for Mode in Statistics

I am looking for some real world examples for mode in Statistics involving topics which students like say Football or Social networks. Also they need to clearly identify differences in the usefulness of mode and mean. For example which player to…
Vrashabh Irde
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Average Growth Rate for Year 1 across 5 groups

Lets suppose that I am measuring the total number of online visitors to 5 websites on a monthly basis. I have this data for the months of Jan - Dec. What I want to understand is "What is average yearly growth rate for the websites?" That is, imagine…
theamateurdataanalyst
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How do I compute the average difference in a list of numbers?

I have a list of numbers: 280, 449, 689, 959, 1360, 1740, 1139 Between 280 and 449, there is a distance of 169, and between 449 and 689, a distance of 240. I need to know how in the simplest way that I can find the average numerical distance…
mcgrailm
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Calculate a Ranking Average?

I got stuck to find a fair formula to calculate the average ranking of the items that I found after consecutive searches, look: If I calculate the simple average of the item2 for example I get 1,33 as a result, not even nearly close to an "average"…
deniswsrosa
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Are these government statistics wrong?

I'm sorry to ask such a basic maths question here, but the reason I'm asking is that just maybe academics apply a different process for averaging out statistics that I don't know about. I need to rely upon the averages in the percent tables on this…
smashingtuck
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