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
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The difference is generally very minor
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'Simple' arithmetic mean is easy to undertand for all people hence why it is commonly used
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If you care so much about geomean than do your own calculations like I did
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There can be cases where data can be skewed/misinterpreted
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Everyone stay safe and take care
I've been looking into the inequality of arithmetic and geometric means, trying to prove it in general for N terms.
Proving it to be true for 2 terms is easy, a little harder with 3 terms, and I quickly run out of patience and paper and sanity for 4 terms. Is there a way to prove it in general for N terms?
The question goes:
The arithmetic average of six natural numbers is 6. What highest possible value some of them can have? (Roughly translated)
a) 20 b) 21 c) 22 d) 23
If a dataset does not follow a particular distribution (e.g. normal, lognormal, etc.), can it be said that the arithmetic mean of all the values in that dataset is not valid (or otherwise reliable)?
Two numbers differs by 40 and their arithmetic mean exceeds their geometric mean by 2.
What is the smaller number? the choices are 45,81,64 and 100, I chose the 100 because its the nearest but Im not sure about my answer :(
Hi! I'm learning the differences of all the means and this question just came to my mind as I learned that geometric mean is a good alternative to compares things from different scales. Most of the tutorials I've read said Geometric mean usually gives the same trend as the normalized arithmetic mean. So are there ever any exceptions where you can't use GM as a substitution for normalized AM? Thanks!
I watched 5 videos on YouTube and I still donβt understand what Iβm supposed to do
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:
| Value | Choice |
|---|---|
| $10 | 0 |
| $20 | 0 |
| $30 | 0 |
| $40 | 1 |
| $50 | 1 |
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!
https://preview.redd.it/7pnde78s99d51.jpg?width=362&format=pjpg&auto=webp&s=a3e21fbccb5d032888aa34e9f02c948d548d652b
http://edspi31415.blogspot.com/2020/07/hp-41c-hp-42s-ti-60-arithmetic.html
Arithmetic-Geometric Mean
The program AGM calculates the arithmetic-geometric mean of two positive integers x and y. As the graphic above suggests, an iterative process is used to find the AGM, computing both the arithmetic mean and geometric mean until the two means converge.
a0 = x
g0 = y
Repeat:
Arithmetic Mean: a1 = (a0 + g0)/2
Geometric Mean: g1 = β(a0 * g0)
Transfer new to old: a0 = a1, g0 = g1
Until |a1 - g1| < tolerance
You can set the tolerance as low as you want. The programs presented on this blog set tolerance at 10^(-10) (1E-10), to fit the calculator's display.
Click on the link above to get the program listings.
- If the sum of the squares of 10 numbers is 645 and their standard deviation is 2.87, find their arithmetic mean.
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.
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?
A<B. Show that A<((a+b)/2)<b
I came up with the following proof, but most of the Youtube video proofs I've found are way more complicated. Am I correct though that this is the proof?
A<(A+B)/2
0<((A+B)/2)-A
0<((A+B)-2A)/2
2*0<((A+B)-2A)/2*2
0<B-A
A<B
Second One:
0<A<B. Show that a<βab<b
I came up with the following proof, but most of the Youtube video proofs I've found are way more complicated. Am I correct though that this is the proof?
a<βab
a^2<(βab)^2
a^2/A<AB/A
a<b
Third One (Harmonic Mean)
0<a<B. H is 1/H=1/2((1/A)+(1/B)) Show that A<H<B
Isolated H=2AB/B+A
A<2AB/B+A<B
A<2AB/B+A
Isolated A<B
Is this the proof?
