
05072006, 10:14 AM

#1

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why averages?????????
if you think about the we base alot of our decisions on all kinds of averages .life expectancy,portfolio returns,inflation.....stop and think for a minute though ..can anything really be average?
if everyone either died at 50 or 100 the average would be 75..but would planning for 75 really help? next stop if you made it to 50 would be 100.......the average american family is 2.6 people....ever meet one of those?
point is it seems that working with averages still dosnt seem to give us to much about what it is we want to know.......
why arent things rated in median? you know ,where the largest group actually ends up landing........
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Re: why averages?????????
05072006, 10:26 AM

#2

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Re: why averages?????????
in statistics medians are a lot mor usefull than averages.
however it is more difficult to compute.
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Re: why averages?????????
05072006, 10:33 AM

#3

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Re: why averages?????????
i would think they would be..at least you know where the majority fell out......to have the market rise 16% most of the time and then fall 16% or so and call it a an 8% average is a pretty wide scarey ride in a way



Re: why averages?????????
05072006, 10:38 AM

#4

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Re: why averages?????????
Who cares about averages or medians? I think most people found this site because that want to ensure that their funds outlast a *worstcase* returns sequence.
Assume that you live for the maximum lifespan (around 120 years), and see if your withdrawal rate and portfolio survive the Great Depression and 70's stagflation.



Re: why averages?????????
05072006, 12:05 PM

#5

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Re: why averages?????????
i think every thing we figure is based on averages....we base our calulations on an average 3% inflation rate,,,an average gain of 4% over the inflation rate,,,a 79 % average return ,,,we cant help but use this thing called an average,we invest in certain index funds so we can use the average they get for our calculations...its making my hair hurt!



Re: why averages?????????
05072006, 12:21 PM

#6

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Re: why averages?????????
The one big revelation in the past decade or two has been that people finally realized that retirment planning shouldn't be done with averages but rather with worst case or at least statistics.
The old approach was to say "Stocks return an average of 10%/year historically, Inflation averages 3% per year, so you can safely spend 7% per year". This was the conventional advice from financial planners up until recently, and there are certainly some financial planners still approach it this way.
If you've been around this board long you know we don't think this way.



Re: why averages?????????
05072006, 01:18 PM

#7

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Re: why averages?????????
while the median is indeed the better measure of "central tendency", the advantage of the mean stems from application of the "central limit theorem" which allows one to easy measure means and standard deviaitons resulting from the sum of independent random variables, as in a portfolio.



Re: why averages?????????
05072006, 01:50 PM

#8

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Re: why averages?????????
Quote:
Originally Posted by mathjak107
i think every thing we figure is based on averages....we base our calulations on an average 3% inflation rate,,,an average gain of 4% over the inflation rate,,,a 79 % average return ,,,we cant help but use this thing called an average,we invest in certain index funds so we can use the average they get for our calculations...its making my hair hurt!

I'm not sure this statement is accurate. While we may talk about averages when posting on these boards, most of us consult historic simulations like FIRECalc or statistical based models when actually developing and validating our plans.
The appeal to index funds isn't based on averages per se, but on the belief that in a highly efficient market the cumulative burden of transaction costs, tax leakages and management fees incurred though active management cannot be overcome by active management.
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Re: why averages?????????
05072006, 01:59 PM

#9

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Re: why averages?????????
Not to mention we're probably very unaverage people (or ARRRE we?) who invest very unaveragely, have a higher than average level of smartiness, and also make up their own words!
So does the law of averages apply to us?
Or is it luck, and we've already used up our lifelong quotient of said luckiness by getting to quit work?
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Re: why averages?????????
05072006, 02:39 PM

#10

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Re: why averages?????????
Quote:
Originally Posted by d
while the median is indeed the better measure of "central tendency", the advantage of the mean stems from application of the "central limit theorem" which allows one to easy measure means and standard deviaitons resulting from the sum of independent random variables, as in a portfolio.

i think theres something to be learned here but im not quite sure what it is?"""""""""""""""""""



Re: why averages?????????
05072006, 02:45 PM

#11

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Re: why averages?????????
Average is not particularly useful without considering the standard deviation?
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Re: why averages?????????
05072006, 04:46 PM

#12

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Re: why averages?????????
Quote:
Originally Posted by mathjak107
i think theres something to be learned here but im not quite sure what it is?

The central limit theorem states that for large enough samples (usually interpreted as greater than 30 observations) the average of sample averages (the mean of the means) follows a normal distribution. With the normal distribution model (you now know the sample mean and standard deviation) you can make inferences about the behavior of the population.
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Re: why averages?????????
05082006, 01:46 PM

#13

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Re: why averages?????????
Flip a coin 10x with heads=1, and tails=0.* In this case the mean is much more useful than the median.
Many probability distributions are defined by the mean, which is sometimes the same as the median.* If you want to estimate the mean from samples, you'd average.
The cool thing about the central limit is that it doesn't even matter what the underlying probability density is. When you add samples the distribution is always normal.. very strange.



Re: why averages?????????
05082006, 02:43 PM

#14

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Re: why averages?????????
the median by definition leaves 50% of the observations to either side, so it is very clear in its meaning (relative to central tendency). the mean is subject to bias from extreme observations and in such cases is not clear in its meaning.* for symmetric distributions the mean and the median will be the same, as is the case in the head/tails example where both =1/2
that the central limit theorem results in an approximately normal distribution without regard to the underlying distributions (if the sample size is sufficiently large) is indeed its great advantage. but it's not strange ... though it might seem so as first glance.
since this thread might already be getting a bit arcane, let me note that the mean is that value which minimizes the sum of squared error (when measured around it), while the median is that value which minimizes the absolute value of the error (when measured around it).* lastly, we should note that the mean is an "expectation", the median is not.



Re: why averages?????????
05092006, 09:24 AM

#15

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Re: why averages?????????
And with that I'm going to take two very large motrin grab a beer, sit in the corner with my pointy hat on, and play with my lower lip.
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Re: why averages?????????
05092006, 11:02 AM

#16

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Re: why averages?????????
Quote:
Originally Posted by mathjak107
* *why arent things rated in median?* *you know ,where the largest group actually ends up landing........

One of the problems is that even the median does not mean itis where the largest group is landing.. that would be the mode....
Let's use your example as before with a slight change.... 49 people die at 50, 40 die at 100... the other two die sometime between 50 and 100... then the MEDIAN is that number... so if the two died at 55.. the medium is 55... if they died at 80, the median is 80... so, what do you learn from this
But, in true stats, the likelyhood of seeing this is low... you do have a bell curve etc... that is why we use averages.



Re: why averages?????????
05092006, 11:31 AM

#17

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Re: why averages?????????
Texas:
The mode is the "most likely" but, in the case of continuous (or near continuous) data is not usually of any use. When categorical data is used, and the number of categories is rather small, it is useful, but differs in interpretaion from both the mean and the median.
In the example you use, the data is clearly bimodal, and NO measure of central tendency is a good descriptor ... but the median will still leave 50% above, and 50% below.



Re: why averages?????????
05092006, 12:24 PM

#18

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Re: why averages?????????
Quote:
Originally Posted by d
Texas:
The mode is the "most likely" but, in the case of continuous (or near continuous) data is not usually of any use. When categorical data is used, and the number of categories is rather small, it is useful, but differs in interpretaion from both the mean and the median.
In the example you use, the data is clearly bimodal, and NO measure of central tendency is a good descriptor ... but the median will still leave 50% above, and 50% below.

D...
I know... I was using an extreme example... a poster had said that the mediun was the most likely to happen... by definition, the mode is the most likely to happen.. definition:
Statistics. The value or item occurring most frequently in a series of observations or statistical data.
My extreme example was to show that median is not always a good indicator if the data is skewed
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