When Should I use the Geometric Mean?

[@nigellovatt9982]

Many thanks. Oybcame across geometric means today and you're the first one infilly understand.

[@deependrapanwar9457]

Thankyou brother for helping me to better understanding of GM.

[@SumriseHD]

Here, take this, this is a space: " " You might want to use it :D Other than that, great video, thank you!

[@hypebeastuchiha9229]

Interesting. Didn’t know this

[@Null_Simplex]

One question I’ve wondered is when to use arithmetic mean vs when to use median. My intuition is that arithmetic mean is useful when you want to run an experiment many times where the trials are independent from one another. This is due to the CLT, making variance (or the covariance matrix in higher dimensions) the “preferred” measure of dispersion for this scenario. Median on the other hand would be useful for when you want to run an experiment a limited number of times, preferably 1, with the measure of dispersion being median distance to the median. This is because these two give you a range that tells you roughly where you’ll end up half the time if you run the experiment, and this range is resilient to outliers so long as you don’t run the experiment too often. Just my guesses.

[@DrBarker]

There are some general rules of thumb, like it might be best to use the median if there are lots of outliers, or if the data is skewed, and better to use the arithmetic mean if there are no outliers and the data is symmetrical.

[@Null_Simplex]

@@DrBarker I have heard these points before, but I wanted to explain my intuition a bit more. It seems median and median absolute deviation from the median do not respond strongly to outliers where as mean and variance do. But what exactly is an outlier? It’s data that is so distant from the other data points that it stands out. Outliers by their nature are rare. Having said that, the more times you run an experiment with independent trials, the more you expect to run into outliers, and thus the more important it is to include them in whatever you are calculating. However if you are running an experiment very limited times, optimally once, you would expect outliers to not play a role due to their rarity. If you sampled the wealth of a few random families in say South Africa, a country with one of the highest wealth inequalities in the world, you’d expect them all to be relatively poor. However, if you ran the experiment enough times you’d eventually get a very wealthy family in the data set. I’m not saying my idea is correct, but wanted to share why I suspect that median and median absolute deviation from the median are better used for a limited number of trials, where as mean and variance are better used for many repeated trials.

[@youssefosama949]

Thank you

[@lasereyes555]

I have a question: If I have multiple Geometric Averages in a portfolio (multiple accounts in a portfolio), can you use the same calculation method to find the geometric average of the portfolio? For example, let's say my portfolio has three accounts: 1) S&P 500 Index Fund, geometric average of 10% 2) Gold Investment, geometric average of 12% 3) Tesla Stock, geometric average of 15% And, I want to find the geometric average of my portfolio. Would this calculation be correct: [(1.10)x(1.12)x(1.15)]^1/3 -1. Thank you for your reply.