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I’m glad it helped!

Geometric mean is really used in an exponential system. In your case, the events could go either way. If you consider them independent, then arithmetic mean would be best. If you consider training to be a factor and want to figure something like the average percent improvement, geometric mean would be a good starting point. I have another video that talks about average rates of change that might be helpful

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Of course! I live to serve.

@@MrPledgerStaysAfterSchool love from india

Multiply all the numbers and take the nth root where n is how many numbers you multiply. 2 numbers will be a square root, 3 numbers a cube root, 4 numbers a 4th root and so on

Good question. If it contains 5 numbers, you'll multiply them and then take the 5th root. For 6, you'll multiply them and then take the 6th root

Thank you, I try!

And thank you for the feedback! I really appreciate it! I'm very happy this was helpful for you. If there's anything else I can help with, just let me know

Okay, so there's a bit to unpack here. You're pretty much dead on in your understanding. Think of a mean as a functional equivalent. Think of arithmetic mean (average). 80, 90, and 100 add up to 270. That is the functional equivalent of adding three of the average, which is 90. ~~> 80 + 90 + 100 = 90 + 90 + 90. Geometric mean is the same way: 80, 90, and 100 multiply to 720,000. Cube root it and you get the geometric mean of about 89.628. So, multiplying 80 × 90 × 100 is the functional equivalent of multiplying three 89.628s. ~~> 80 × 90 × 100 = 89.628 × 89.628 × 89.628 (off only because of rounding). Annual rate of return is an extension of this, the only difference being that you start from a different number. I'll just make up some numbers here. You start with $1,000 and your returns are up 5%, down 2% and up 3%. My multipliers are 1.05, 0.98, and 1.03, respectively. 1.05 × 0.98 × 1.03 = 1.05987. The geometric mean is 1.01957. Remember, it's a functional equivalent. 1.05 × 0.98 × 1.03 = 1.01957 × 1.01957 × 1.01957. Because 1.01957 is the multiplier for a gain of 1.957%, we can say that "we essentially gained 1.957% each year for three years." Here's the math: $1,000 × 1.05 × 0.98 × 1.03 = $1,059.87 $1,000 × 1.01957 × 1.01957 × 1.01957 = $1,059.87 Now to your last question, yes, you are correct. If you're compounded annually and your time is greater than one year, compound interest will ALWAYS be more than simple interest.

I'd be happy to! Do you have any particular topics of interest?

Thank you, I glad I could help!

Thanksyou somuch.. its a bighelp

Sometimes im very curious regarding square root🤣 sorry to tell about this can you add more and explanation regarding this matter

Of course! Anytime

The reply to this would take longer than I can fit in the comments, but as long as one of the numbers is positive and none of them is negative, the arithmetic mean is ALWAYS greater than the geometric mean. The Wikipedia page actually has a pretty good proof right at the top. Hope it helps. en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means

My pleasure!

Glad it helped!

Thank you!

Thank you!

Of course, it's my pleasure!

The GCF *is* 3 x 3 x 2, or 18. To find the LCM, you can multiply the 18 by the 2 left over on 36 to *get* 36. Or, you can multiply 36 by nothing, because nothing is what’s left on the 18, and it *stays* 36. I hope that helped. Good luck on your test!

Kevin Pledger thanks so much I got a A on my test

@@mayhaan4004 Good job! I'm very happy for you!

Good question! Since geometric mean is an average *factor*, you would *multiply* year 3 by the geometric mean to get a prediction for year 4.

@@MrPledgerStaysAfterSchool I appreciate your help :)

@@adrianaamaya396 Of course, anytime!

@@MrPledgerStaysAfterSchool Hey, I have a question here. The geometric mean I got would help me understand at what average rate 1000 compounded in 3 years and grew to 1330 and I can verify the same by multiplying the very first investment (i.e.,1000) to the geometric mean (1.0997) raised to power 3. But since our annual return is not actually constant and geometric mean is just an annual average factor, there are high chances that the prediction for year 4 would not be accurate. What purpose does it even serve then? JUst curious.

You're very welcome. I am glad I could help!

Thank you for your comment. I understand what you’re saying, and I could go faster, but a lot of people need me to go slowly through how to do these so that they have time to process it before I move on to the next thing. Have a good day!

Kevin Pledger understandable, thank you

Thank you for the comment! It's my pleasure!

Omega Ultra Gee, thanks.

No offense!

This is true, and by using factor pairs, you can see that 15 is the biggest number that is in both lists. My method is an alternative to factor pairs. 15 = 3 × 5 60 = 2 × 2 × 3 × 5 Because both have 3 × 5, and because 3 × 5 = 15, you can see that the GCF is 15 here too. The advantage of mine is that it shows you LCM is 60 by telling you to multiply 15 by the leftover 2 × 2. Does this help?

My pleasure. I'm glad it was helpful!

I'm really glad it was helpful for you!