Arithmetic Mean, Geometric Mean, Median or Standard Variance?

Say I started with $100.

1st Year = $135

2nd Year = $182.25

3rd Year = 54.675

100-54.675 = 45.325 = loss / 3 = roughly 15 = annual loss.

Arthemtic Mean is 0 so thats no good.

Median is 35 so thats no good.

Standard Variance doesn't measure central tendency.

Geometric Mean yields 44 so where am I going wrong?

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    $\begingroup$ I obtain -18% for the geometric mean return ($100(1 - (1.35\times1.35\times0.30)^{1/3})$). How do you obtain 44? $\endgroup$ – whuber Oct 30 at 21:53
  • $\begingroup$ Hey thanks for helping. Isn't the formula (35 * 35 * 70)^(1/3)? I thought I had to multiply all the numbers and n root it $\endgroup$ – Benny Oct 30 at 21:54
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    $\begingroup$ You seem to be treating a loss of 70% as if it were a gain of 70%! (I wish I could do that with my investments ...) $\endgroup$ – whuber Oct 30 at 21:55
  • $\begingroup$ Oh i c now..wow thanks for ur help. $\endgroup$ – Benny Oct 30 at 21:56
  • $\begingroup$ Just to make sure, I can't measure central tendency with standard variance, correct? $\endgroup$ – Benny Oct 30 at 21:58

Take the geometric mean not of 35% and 35% and -70% but rather of (1+.35),(1+.35) and (1-.70) which works out to be the cube root of .54675 which is 0.8177..... This is a per annum loss of 18.23%. So, over three years, thinking that the annual loss just adds up, end up with a three-year loss of 54.69% instead of the actual loss of 45.325% (close enough to 54,69% for gummint purposes). I remind those who are horrified by the cavalier addition of the annual losses to get the three-year loss that many newbies to the stock market (and many seasoned shills too) are quite happy to believe (or aver to the newbie) that a 50% gain one year followed by a 50% loss means that at the end of two years, the investment has not lost any value.

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