The Geometric Mean

[JasonBallard]

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.

[avaition]

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

[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 :)

[claudeh.]

thanks dude i might just pass my freshman year

[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 

[aqsazubair]

your method of teaching is clean and super

[Maxdwolf]

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

[nathanz]

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

[chrisrosenkreuz]

thanks for the 'ratios' bit it gives good perspective

[RLLY]

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

[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! :)

[sandraswan]

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

[wrednymaz]

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

[danieljacobsen]

Thanks, man! You're a great teacher!

[BicycleFunk]

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

[shrey_bruh]

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

[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.

[심녹차]

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

[marconie]

Very simple, very easy to understand. Thanks

[subhamoymondal]

Easy, simple, vivid...nice explanation