Now it all comes back to me. I remember why I hated my statistics
courses!!!!!!!!!!
This is getting worse than the "How many PWP's does it take to change a
light bulb". Only kidding and LOL!

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> ----------
> From:         Gil Lieberman[SMTP:[log in to unmask]]
> Sent:         Sunday, September 13, 1998 1:57 PM
> To:   Multiple recipients of list PARKINSN
> Subject:      Median is not average
>
> Dear listmembers,
> I have some comments re Dennis Greene's discussion below
> based on what I learned about statistics terminology fifty years ago.
>
> There are four concepts which need to be considered:
> 1.The definition of a measurement modeled mathematically as a random
> variable.X
> 2.The probability distribution of X.
> 3.Measures of central tendency of the probability distribution of X.
> 4.The populations from which the measurements were made.
> The terms measurement and observation are used interchangably.
>
> The median of X is defined as the 50 percent point of the probability
> distribution.
> It is estimated from a finite set of data by finding a number  for
> which half
> the data is larger and half the data is smaller.
>
> The term average is a general term referring to a measure of central
> tendency of
> the probability distribution of X.Usually,the term average refers
> specifically to
> the arithmetic mean of a set of measurments of X,but it could refer to
> the
> median,
> to half the difference between the largest and smallest measurement,to
> the
> square
> root of the product of the largest and smallest measurement(a
> geometric
> average),
> the difference between the 75 percent point and 25 percent point,the
> most
> probable
> value of the probability distribution and so on.
> Depending upon the shape of the underlying probability
> distribution,these
> averages
> can be vitually the same or quite different.Thus for a Gaussian
> distribution,the mean,median,
> and most-probable values are the same because it is a well-behaved
> symmetric
> distribution,whereas
> for a nonsymmetric distribution,they will generally be significantly
> different.There are
> nonwell-behaved symmetric distributions such as the Cauchy
> distribution for
> which the arithmetic
> mean is virtually useless,whereas the median or most-probable values
> contain
> more useful
> information about the data.
>
> Finally,the usual basic assumption of the data is that the
> observations were
> made from the same
> population.The model is one of a set of observations under similar
> conditions.If however,
> the observations are based on sampling from more than one
> population,then it
> is possible
> that the probability distribution will not have a single peak and
> therefore
> may not have a
> unique most-probable value.How the observations are defined determines
> the
> statistical
> properties of the random variable X.
>
> Now to Dennis's discussion below.
> Par.1:Based on the above,a median is an average,but an average is not
> necessarily
>       a median.However,by definition,the median does split the
> observed
> population in two.
> Par.2:Since for nonsymmetric distributions,the arithmetic mean and
> most
> likely values
>       are not the same,sentence one is incorrect since by
> average,Dennis is
> referring
>       to the arithmetic mean.The last sentence touches on the concept
> of
> population.
>       One population could be the population of PWPs.Another could be
> the
> population of
>       ages at which these PWPs experienced onset.But Dennis confuses
> this
> disinction.
> Par.3:This confusion is continued here.Furthermore,the definition of
> median
> used here
>       is incorrect.The calculation of a median is based on the
> complete data
> set,not
>       just on the minimum and maximum values.For example,given 101
> data
> points,the
>       median is calculated by ordering the numbers.The median is the
> number
> such that
>       50 numbers are larger and 50 numbers smaller.
> -------------------------------------------------------
> Date:    Sat, 12 Sep 1998 08:09:58 +0800
> From:    Dennis Greene <[log in to unmask]>
> Subject: Median is not average
>
> Several recent postings have mentioned that 57 is considered the
> median age
> for the onset of PD.  As far as I can see most have assumed that
> "median"
> and "average" mean the same thing and have concluded from this that
> half of
> the PD population are under the age of 57.  However median and average
> are
> not the same thing, nor can you use either of them to conclude that
> half the
> PD population are under 57.
>
>  An  average age for something to happen tells you at what age the
> event is
> most likely to happen. In our case it would be calculated by adding up
> the
> age at onset of every PWP, and then dividing the total by the number
> of PWP
> (several million bits of information processed).  Even if 57 were the
> average age, it would mean that 57 was the age at which most people
> experienced onset and consequently most PWP are older than 57.
>
> Median refers to the age itself, not to the numbers afflicted.   It is
> derived by finding the middle point between the age of the youngest
> and
> oldest age of onset (two bits of information processed). To have any
> meaning
> at all, a median value would need to be quoted in its context.  By
> itself
> the statement "the median age of onset is 57" tells us very little.
> It
> would be true in both the following cases:
>
> 1.    Youngest age of onset = 50
>        Oldest age of onset  = 64
>        Median age of onset = 57
>
> 2.    Youngest age of onset = 20
>        Oldest age of onset =  94
>        Median age of onset = 57
>
>
> Dennis
>
> +++++++++++++++++++++++++++
> Dennis Greene 48/11
>
> "It is better to be a crystal and be broken,
> Than to remain perfect like a tile upon the housetop."
>
> [log in to unmask]
> http://members.networx.net.au/~dennisg/
> +++++++++++++++++++++++++++
>