The Geometric Mean

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! The Geometric Mean. In this video, I show how to find the geometric mean of two numbers and show what that number means in relation to the numbers that you started with.

[@JasonBallard81]

The geometric mean is generally used with time series data like calculating investment returns because the geometric mean accounts for the compounding of returns. Because of the effect of compounding the geometric return is always less than or equal to the arithmetic mean return.
Consider the video's example. Lets say you have $100 to invest. Lets say you earn $4 the first year and $9 the second year. The arithmetic mean says you earn $4 on the $100 investment the first year and $9 on the $100 investment the second year. Resulting in an arithmetic mean of $6.5 for two years.
The geometric mean considers growth or compounding returns. Using the same example above...The geometric mean says you earn $4 on the $100 investment the first year and $9 on the $104 investment the second year. Resulting in a geometric mean of $6 for two years.
Notice the difference? The geometric mean return assumes that the investment amount is not reset at the beginning of each year and, in effect, accounts for the compounding of returns.

[@pneron2032]

Thank-you. Exactly what I was hoping to find in the comments.

[@AAA11546]

Thanks man, this is great!

[@sukursukur3617]

This usage area didnt satisfy me

[@avaition321]

Simple, clear, concise, and, in the end, a Big THANK YOU for posting

[@sambhavjha3641]

hey are u still alive?

[@claudeh.8145]

thanks dude i might just pass my freshman year

[@tarsemsingh4696]

Hlo how was your paper more theory or more sum . Can you tell me important question .reply

[@ThelolArtist]

hoping ur doing well as a senior now

[@claudeh.8145]

@@ThelolArtist thanks :)

[@nelsonagholor1097]

Claude H. hope u get to graduate

[@sarb1943]

Yeah I'm taking a geometry test rn and I'm FUCKING CONFUSED😂

[@aqsazubair4530]

your method of teaching is clean and super

[@fantasyspiritt]

Graduated from Duke studying engineering last summer and your videos saved my ass!
I'm studying for CFA now, and I'm still watching your vids. You're awesome! Thank you :)

[@sandraswan1977]

so far I learned how to find the mean, and standard deviation. Now I'm on stem plot. yaaayyyyyyy

[@chrisrosenkreuz23]

thanks for the 'ratios' bit it gives good perspective

[@danieljacobsen6766]

Thanks, man! You're a great teacher!

[@janepianotutorials]

Hi Patrick, I was going to start a series of lessons on geometric calculus, and for curiosity checked to see whether there was anything on YT on just the geometric average. That what precipitated this message. There is an important system of calculus based on the geometric average. It is called the *geometric* (misnamed by early users as multiplicative and the name stuck) calculus. It is one of many non-Newtonian calculi (NNC). Scientists have found nontrivial applications. There is a little about NNC on my website and free download links to the books are provided. The *bigeometric* calculus uses the geometric average on both axes. I think this will be the most important one because it is scale-free. It is being used in fractal research to measure roughness. If you want to make tutorials of NNC, that'll be great. You'll be the first to do so (I'll let you beat me to it if you wish). I've seen many of your math tutorials and trust that you will do a good job! :)

[@janepianotutorials]

No response from Patrick. To those "plus one"-ing my comment. Made two intro lessons. Click my name > website > NNC in sidebar

[@R31LLY34]

You're actually a wizard. Thanks for the help, keep up the great videos!

[@patrickjmt]

@H20QuincyAlpha working on it! : )

[@nathanz602]

In 18 seconds I now know exactly what to do.... Thank you.👍👍

[@Maxdwolf]

That's the first time I've ever had the significance of the geometric mean explained. Thanks.

[@CuiHu]

earlier today my teacher taught my class this lesson and it just flew over my head and now you just tied it all back together thank you very much

[@shrey_bruh774]

OMG !!!! U are awesome at explaining and keeping peoples interest in the video with u ....thanks for posting such an awesome vid....

[@subhamoymondal4152]

Easy,simple,vivid...nice explanation

[@wrednymaz]

You are great. Thumbs up! Most college professors take forever to explain this with poor results.

[@taylorjackson8358]

This video helped me a lot on my final review thank you soooo much

[@huenhuluu]

Great explanation. Thank you.

[@hope-a-dope7300]

This was very helpful thank you

[@elmolover2458]

does this also work for numbers greater than lets say between 50 and 700. do you just multiply the 2 numbres and find the square root ???

[@bluesbender69]

Thank you for posting this.

[@nouf6201]

Thank you very much ! That was so helpful

[@Cosmo_P0litan]

This is a fantastic video, well done!

[@marconie3901]

Very simple, very easy to understand. Thanks

[@patrickjmt]

you are most welcome!

[@ellinosgold8198]

Hi sir Patrick! You really helped me especially in my assignments.. I am a 10th grade student and your tutorials make me understand some difficult parts in our topic like those geometric and arithmetic means.. hoping that you'll discuss more about the said topics.. ^_^

[@ultimateyrd2197]

Thank you man very helpful

[@karthik2k2]

Thanks a lot patrick! Got a doubt- What is the advantage of calculating geometric mean over arithmetic mean?

[@zingzing47]

Great Video. This is very helpful

[@BronsonFan111]

Wow it's that simple. Thank you very much Patrick. :D

[@tokyoghoul8958]

Congrats 🔥🔥🔥 1 million

[@MarleyMicmuffin]

thank you for helping with my homework!

[@BicycleFunk]

So cool! Schools should literally just use your videos and spend lecture time solving problems or in discussion.

[@zia7040]

thank you.

[@philippaige7359]

geometry exam tomorrow....... you really saved my butt dude! Thanks!

[@jjolly1414]

thanks, found it helpful

[@user-fy8cj5ub1v]

So easy. In the book it was so difficult. You make it so easy

[@DoujinReader]

Thnx had to figure this out fast

[@aznpiccplayer123]

@kalvianss I remember in geometry five years ago that it's used to find the volume of a frustum, and from statistics a few months ago, you use it in special cases of approximations. That's all I know about it, but there's probably a lot more on Wikipedia and other sites.

[@usmanmehmood7614]

salute to u sir well explained

[@jessmaster1175]

thx that was really helpful

[@Maxdwolf]

@Maxdwolf Occurred to me the ratio trick only happens w. 2 numbers (and even then a pretty solution means picking the right 2). It's still about ratios and thus applicable to exponential growth and the like of course.

[@chandrasekar4252]

......

[@exo-l1472]

I'm always late in class so I can't catch up with some lessons.So this kinda help me alot.Thank you very much.😄

[@yesipan]

kpop?

[@zubayirhkazi9115]

kpop sucks

[@annas4392]

Thank you!

[@DVincent1231]

@patrickJMT I did find this helpful, however what happens when there is a negative number. I was given an example in class, to find the geometric mean of 10%, -14.55% and 14%. what would be the geometric mean of these three figures.

[@nkiruogene]

Thank you so much.

[@ldiazmdiaz]

To me it also means that 4x9=36 is a rectangular shape, but if you want to covert it as a perfect square you take the Geometric mean of it like the( square root of 4x9=6) and that is a 6x6=36 a perfect square. It a rectangular to a square converter.

[@seifdeiab]

How many types of "mean" we have? Could you list all of them? Or there are only 2?

[@MrAthleticKid]

thanks this really helps

[@swarupmajumdar5262]

Thank you sir... i have a new thought for you

[@XxHamletJacobsXx2022]

Thank you very much!!! Keep up the good work :-)

[@SanoriZena]

lol thank you! My math teacher could not explain this!

[@user-mr3wf3xy4t]

is geometric mean in triangles, the same with geometric means without the triangles???

[@666meowth]

Thank you!

[@behnamasid]

Could you make a video about harmonic mean, or just tell me what harmonic mean is? thanks

[@tigab37]

you explained that better and 20 times quicker than my algebra teacher

[@shanesnyder6750]

Thanks, I understood it within the first 16 seconds of the video.

[@cb2738]

Lol nioce

[@muhammadadnan0075]

what is the name of playlist? i can't seem to find it.

[@ujjalsantra7554]

Thank you sir

[@jeffreypritchard6102]

Geomean really comes in handy when calculating investment returns.

[@gpspakkuwaitmills3830]

Thanks for making me understand this...from Pakistan

[@melariemantanona2316]

A problem like this came up randomly in my Precalculus book in the Sequences, Series and Probability chapter and I had to search it up to double check if it was just this easy. Haha

[@danielt2713]

I get in now. Fantastic

[@livinindubai]

If you are taking requests I would wish for a video explaining why in some cases geometric mean is preferred over arithematic / weighted avergae

[@ravian1990ca]

good job u made life simple

[@Adam-wt9gh]

hey patrickJMT, my teacher gave me a problem with a right triangle and in the directions it says "Find the length of the altitude drawn to the hypotenuse if AD= 4 and DC= 16". She told me to use the Geometric mean. I don't see how that is possible, if you can explain that would be greatly appreciated!

[@HelneitCo]

Helpful video!
However, your example has used only two numbers.
How will the logic work if you are to say, find the geometric mean of more than 2 numbers?
Thanks

[@taylorhentsch999]

AbeIAMNOTAHUmANPTII Masaryk it would be to the cubed root. (x*y*z) ^(1/3)
(product of n values) ^(1/n)

[@HelneitCo]

AbeIAMNOTAHUmANPTII Masaryk Thanks!

[@adaezechukwukere8006]

thank alot i understand it now :)

[@sathwikgumpina3519]

Very good work

[@patrickjmt]

Thanks

[@gj9665]

Great vid

[@magicguy1988]

So if I have three numbers, A B C then their geometric mean is (A*B*C)^(1/2)? Or is this true for only two numbers?

[@arjelinecaloring1217]

Thankyousomuchhhh!!!

[@saadnadaf8753]

Thanks dude

[@niathedland4428]

Thank you

[@yuechen2421]

How about 3 values of geometric mean? What is that number mean?

[@HotPepperLala]

Oh my god a new video finally

[@NarutoBosslv100]

cool u explained it well

[@amjPeace]

Same as kalvianss, I am looking for some kind of word problem that would be solved using the geometric means, please.

[@lilykenwood5423]

thanks do much!

[@aliafatima9463]

Hiii...I'm from INDIA....GREAT JOB MAN.....😍😍😀😊

[@patrickjmt]

Thank you so much 😀

[@Adobooperator]

wait why did u divide by 2 at 2:33?

[@sohampatil7961]

Nice one you are awesome

[@amdyl]

I'm over here thinking, "How does 2 and 18 get the answer 6?!" But it all makes sense now, thanks!

[@MichaelPari]

thanks bro

[@sambhavjha3641]

thanks patrick
\

[@audreyhill3560]

what if you already know the geometric mean but don't know the other numbers? how do you find that?

[@GiorgioCapocasa]

Wups, I read the Geometric MAN: that would have been awesome.
Still, very good explanation (:

[@laurennicole8987]

This saved me

[@saiyannpishh]

Your initial GM is 2.8 feet. After a day’s steaming at sea, you have free surface in tank measuring 60 feet long and 50 feet wide. The vessel displaces 25,000 T. The S.G. of the liquid in the tank is 0.98. What is the available GM?

[@juanpedro19840914]

In Spanish they are named "Media Aritmética" and "Media Proporcional".

[@GirlsareDown]

I just learned this in 15 seconds... WOW

[@mariammagdyahmed5253]

Postive or negtive six because it's square root isn't it?

[@RealMissCash]

would've been great to show geometric mean of 3+ numbers.

[@deoayo2016]

thx bro

[@SidraRamzan11]

The best Ever

[@ianzhang4914]

Thanks

[@yeeted9098]

Itachi thanks you

[@LovelySteph]

i wish they explained it that clearly in the book.

[@pingier2958]

Thanks bud

[@stopmdot]

@WestyPS360
congratulations