Recently there has been a discussion about whether to use arithmetic mean or geometric mean to calculate the averages when comparing cpu/gpu frame averages against each other. I think it may be good to put the numbers out in the open so everyone can see the impact of using either:

Using this video showing 16 game average data by Harbor Hardware Unboxed, I have drawn up this table.

The differences are... minor. 1.7% is the highest difference in this data set between using geo or arith mean. Not a huge difference...

NOW, the interesting part is I think there might be cases where the differences are bigger and data could be misinterpreted:

Let's say in Game 7 the 10900k only scores 300 frames because Intel, using the arithmetic mean now shows an almost 11 frame difference compared to the 5600x but the geo mean shows 3.3 frame difference (3% difference compared to 0.3%)

So ye... just putting it out there so everyone has a clearer idea what the numbers look like. Please let me know if you see anything weird or this does not belong here, I lack caffeine to operate at 100%.

Cheers mates.

Edit: I am a big fan of using geo means, but I understand why the industry standard is to use the 'simple' arithmetic mean of adding everything up and dividing by sample size; it is the method everyone is most familiar with. Imagine trying to explain the geometric mean to all your followers and receiving comments in every video such as 'YOU DOIN IT WRONG!!'. Also in case someone states that i am trying to defend HU; I am no diehard fan of HU, i watch their videos from time to time and you can search my reddit history to show that i frequently criticise their views and opinions.

TL:DR

• The difference is generally very minor

• 'Simple' arithmetic mean is easy to undertand for all people hence why it is commonly used

• If you care so much about geomean than do your own calculations like I did

• There can be cases where data can be skewed/misinterpreted

• Everyone stay safe and take care

EDIT:

THREAD CLOSED. It turned out that I was asking the wrong questions. I have to rethink my game review score system. I guess that I'll define the percentage each criterion has for the final score, that seems to make the most sense.

Thanks, all who participated.

EDIT:

After some discussion, this is the state of things: http://postimg.org/image/j87z92ppv/full/ (Imgur did not load.)

Just think about it like this: There's a game with great gameplay (3) but a bad interface (1). For enjoyment of the product, the interface doesn't matter at all in this case, so I'd give the game a "3" in total.

What if the interface was just as important? Then the review score would be (1+3)/2 = 2.

What if the interface score should be considered with half instead of full importance? Should the review score be 2.5 or 2.33...? (I don't care what the outcome looks like, I'm not gunning for neat looking score. I'm still researching my review system.)

It's easy with just two numbers:

[EDIT: Escaped the *.] 3 + (0.5*1 + 0.5*3) = 5, now dividing this by the amount of numbers (2), we get 2.5 as expected. I just simulated the "1" being a half transparent image being overlaid over the solid "3".

"Why what huh?" Well, let's say we calculate the arithmetic mean of 3 and 1. (3+1)/2=2. Let's say we do this while giving the number "1" the information-weight of zero: The outcome would of course be 3. The 3 would be dominant. So, if "1" has the weight 0.5, the outcome should be 2.5

The problem is: How to do this for a bunch of numbers at once?

I know I once cracked that nut, but I just can't remember or find the right idea now. It will be part of a Java program to calculate game review scores from individual weighted criteria. Just so you know that I am rather interested in simple algorithmic statements than in magic math symbols/terms which are rather cryptic to me.

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Im a philosophy guy. I have solid math skills. Im better at stupid little numerical puzzles than my Maths/Engineering friend. But he told me one day, when I was thought bubbling out loud about philosophy of mathematics, that I didnt know enought about arithmetic. This has always gnawed at me. I dont really know what it means to have a theoretical grasp of arithmetic beyond being able to do arithmetic, which I have no problem with. So thats my question. What does it mean to have a complete understanding of arithmetic? Do we need to go back to logic? Or is Arithmetic fully knowable without reference to anything more basic?

Bonus question: Is arithmetic in fact the first stage of mathematics? Or is it geometry along the lines of Greek thinking? Is there an academic consensus on this?

Hi! I am trying to analyze the experimental data that involves choices and values associated with them. My dataframe looks like this:

My goal is to take the arithmetic mean of two value when the responses switch from 0 to 1 (so in this case, (40 + 30)/2 = 35 for this participant/delay combination). I'm struggling to find a programmatic way of doing this. Any help would be greatly appreciated!

69. If the sum of the squares of 10 numbers is 645 and their standard deviation is 2.87, find their arithmetic mean.

Got from Common data set Why is unweighted more important that weighted (UC Davis)

I have data that looks like this: https://imgur.com/a/1hOsFpF

The first dataset is a standard format dataset which contains a list of people and their financial properties.

The second dataset contains "relationships" between these people - how much they paid to each other, and how much they owe each other.

I am interested learning more about network and graph based clustering - but I am trying to better understand what type of situations require network based clustering, i.e. I don't want to use graph clustering where its not required (avoid a "square peg round hole" type situation).

Using R, first I created some fake data: library(corrr) library(dplyr) library(igraph) library(visNetwork) library(stats)

create first data set

Personal_Information <- data.frame(

"name" = c("John", "Jack", "Jason", "Jim", "Julian", "Jack", "Jake", "Joseph"),

"age" = c("41","33","24","66","21","66","29", "50"),

"salary" = c("50000","20000","18000","66000","77000","0","55000","40000"),

"debt" = c("10000","5000","4000","0","20000","5000","0","1000"

)

Personal_Information$age = as.numeric(Personal_Information$age) Personal_Information$salary = as.numeric(Personal_Information$salary) Personal_Information$debt = as.numeric(Personal_Information$debt)

create second data set

Relationship_Information <-data.frame(

"name_a" = c("John","John","John","Jack","Jack","Jack","Jason","Jason","Jim","Jim","Jim","Julian","Jake","Joseph","Joseph"), "name_b" = c("Jack", "Jason", "Joseph", "John", "Julian","Jim","Jim", "Joseph", "Jack", "Julian", "John", "Joseph", "John", "Jim", "John"), "how_much_they_owe_each_other" = c("10000","20000","60000","10000","40000","8000","0","50000","6000","2000","10000","10000","50000","12000","0"), "how_much_they_paid_each_other" = c("5000","40000","120000","20000","20000","8000","0","20000","12000","0","0","0","50000","0","0") )

Relationship_Information$how_much_they_owe_each_other = as.numeric(Relationship_Information$how_much_they_owe_each_other) Relationship_Information$how_much_they_paid_each_other = as.numeric(Relationship_Information$how_much_they_paid_each_other) Then, I ran a standard K-Means Clustering algorithm (on the first dataset) and plotted the results:

Method 1 : simple k means analysis with 2 clusters on Personal Information dataset

cl <- kmeans(Personal_Information[,c(2:4)], 2) plot(Personal_Information, col = cl$cluster) points(cl$centers, col = 1:2, pch = 8, cex = 2) This is how I normally would have treated this

The question actually asks to 'explain' but I can't think of an intuitive explanation.

So I try and simplify sqrt(xy) <= (x+y)/2

(Note x,y bigger 0)

I tried rearranging but didn't get anywhere.

Then I tried using y=cx (c>0):

Sqrt(xcx) <= (x+cx)/2

x sqrt(c) <= x (1+c)/2

sqrt(c) < (1+c)/2

That looks better! But I'm not sure where to go from there, rearranging I get to a quadratic:

0 <= c^2 - 2c + 1

solution c=1, which makes sense, but I don't see how that helps showing the inequality holds? I feel like I'm missing some final step to conclude the proof.

Hey y'all, I am a Pharmacology major and was doing some HPLC analysis. For one of our post-lab questions, it says to generate a calibration curve for these data (use a simple linear fit with no weighting). I'm using excel to plot my graph so does using a simple linear fit with no weighting just mean not using a trend-line?

Thanks!

I have a very small sample of 9 measurements, and noted that the higher measurements correlated with a lower score on another test for those individuals. Therefore I decided to try a weighted mean.

I have a mean of 17.4 and weighted mean of 11.5 for my measurements, but I would love to deliver this weighted mean with a confidence interval. How would I go about calculating this?

The limit as x approaches infinity of 2*x*AGM(1, 2^(-x))*Ln(2) = Pi , and also that the limit as x goes to infinity of 2*Ln(x)*AGM(1, 4/x) = Pi.

It was the clean connection I was looking for between AGM's and Pi, and is a good introduction to lemniscates.

I've found students understand logarithms easier than lemniscates... thought I'd share.

This is more for my own interest than anything else. I recently got back my second stats assessment and was (marginally) above the median and mean mark in both. My brain was happy at the thought of supposedly finishing in the top half overall, but then I got thinking about whether this was necessarily the case. So my question is; is it? Can you finish above the median mark for both assessments but in the bottom half for the two as an average? What about for the mean?

I am tracking animals, and I am interested in taking the average of their lat/long coordinates for a location when they are in the same spot, so as to increase the accuracy of the coordinates for that spot, and to accurately only plot one point on my map for that spot.

I have utilized my field data to assign a Rock ID to each location used by an animal at a site (see these two threads for more on that : https://www.reddit.com/r/excel/comments/eep7dw/how_to_use_a_formula_to_assign_a_row_a_unique_id/

https://www.reddit.com/r/excel/comments/ejhpn5/how_to_determine_when_the_first_occurrence_of_a/ )

My question is , using a formula like this:

=AVERAGEIF(Master!M:M,Master!R:R, H1) - I'd like to tell excel to take the average of my latitude column from all entries that have their test_rock_id column matching the rock-id in cell H1, for example. But, how can I add a weighted average component to this? Specifically, I would like to weight these mean based on the integer values in an accuracy column, where the more accurate the GPS was that day - the smaller the number would be. For example I would like to weight an accuracy of 3 meters higher than an accuracy of 10 meters.

I am not sure how to go about this since most weighted averages are based on percentages, not integers, and if they are based on integers they typically give more weight to higher values, not smaller values.

Thank you!

Hi! I need help with a proof. Sorry about the poor format. I tried to post a photo of the question, but couldn't figure out how.

If A1 and b1 are given positive numbers, with a1<b1, and two sequences of positive numbers are defined by:

A n+1=Sqrt(AnBn) [<- Geometric Mean]

and

B n+1=1/2(An+Bn) [<-Arithmetic mean]

Prove that 0<An<A n+1<Bn+1<Bn

The answer says "needs Geometric mean < Arithmetic Mean, and induction." The induction is where I get lost. I understand the concept of mathematical induction, but I don't see how to apply it here. All I can get is:

A n+1= G

B n+1=A

G<A

and the 2 sequences are positive, so

0<An+1<Bn+1

How do I get the An and Bn in there?

So, I have the recurring formula...

Xn = 1/2 (Xn-1 + (a/Xn-1)) with a being any positive real number.

This finds the square root of a. using the arithmetic mean - geometric mean inequality...

((x+y)/2 > or equal to sqrt(xy))

i must show that

Xn >(or equal to) sqrt(a).

this question isn't worth very much so I feel like I am missing something fairly obvious but I cannot see any answer through manipulation.

formatting: no subscripts so I compromised with Xn and Xn-1. Hope all is clear

edit: sign error

Hello,

In visual builder I created a few series, almost identical but each one with a different offset, in order to compare the day to day differences.

I'd like to know if it's possible to get an additional time serie with the average of the other series.

Using the offset inside the Math aggregation would also be a solution, but I don't know how to implement it.

Thank You in advance,

Given a set of positive numbers A, when is the geometric mean of the harmonic mean of A and the arithmetic mean of A equal to the geometric mean of A? This doesn't always happen, as one can see with the example A={1,2,3}. But one interesting case where it does happen is when the set A is the set of positive divisors of an integer. In this case, the harmonic mean is exactly (n tau(n))/sigma(n), the geometric mean is exactly n^{1/2} and the arithmetic mean is exactly sigma(n)/tau(n). Here tau(n) is the number of positive divisors of n and sigma(n) is the sum of the positive divisors. One can construct other examples from these by multiplying everything in the set A by a scaling factor. Do all such examples arise from scaling a set of a divisors this way? If not, is there a nice characterization of these sets?

https://preview.redd.it/cbmdgykf0t041.png?width=940&format=png&auto=webp&s=50ffdcbb5b3e7c035a2d1f8e5b9b0380b9a48c2e

I have a table of auctions, and am looking for the smartest way to get mean value per certain item ids.
The data will be presented to me the way that there's Quantity and Total price of an auction.

In this example I have expanded the auctions of item id 101 to Column G. Therefore it's now easy to get TRIMMEAN from the whole column. ( based on data from only first 13 auctions though )

The problem is that these auction tables can be tens of thousands rows long, so I don't know even where to start and was hoping if anyone here is able to push me to right direction for getting started. Any help will be greatly appreciated! Thanks in advance.

Non-zero numbers a, b, c, d, e form an arithmetic progression. If

(b+d)/2 + (a+e)/4 = kc

find the value of k.

The explanation for this one was that by the definition of the AM we have

(b+d)/2 + (a+e)2 = c

and from here

(b+d)/2 + (a+e)/4 = c + c/2 => k = 3/2.

But I don't see how this is true unless (b+d) = (a+e)? How is this (b+d)/2 + (a+e)2 = c ture otherwise?