Re: <?????Nora Baron???????>

From: Christian Bau (christian.bau_at_cbau.freeserve.co.uk)
Date: 03/15/05 

Date: Tue, 15 Mar 2005 22:38:13 +0000

In article <1110924697.232654.62580@o13g2000cwo.googlegroups.com>,
 "Randy Poe" <poespam-trap@yahoo.com> wrote:

> Dark Angel wrote:
> > Thank you so very much for your guidance. I was a tad mixed up
> between
> > mean and median. I think I understand better now.
> >
> > ~Dark~
> >
> > Ref: My Question
> >
> > Can someone please explain how to approach this problem without
> giving
> > me
> > the answer. Thanks in advance !
> >
> > Q1.
> >
> > The Internal Revenue Service reports that in 1998 about 124 million
> > individual income tax returns showed adjusted gross income (AGI)
> greater
> > than 0. The mean and median AGI on these tax returns were $25,491 and
>
> > $44,186. Which of these numbers is the mean and which is the median?
> How
> > do
> > you know?
>
> Insufficient information, without knowing more about the
> distribution. Is there a picture that goes with this
> question? Or is there other information?

Without knowing the distribution of salaries, it seems highly unlikely
that the median is $44,186 and the average is $25,491.

The population can be split into two sets of equal size, with all
members of the first set having a salary >= $44,186, and all members of
the second set having a salary <= $44,186.

Let X be the average salary in the first set, and Y be the average
salary in the second set. Then (X + Y)/2 = $25,491 or X+Y = $50,982.

That would mean that salaries are mostly either just very slightly above
$44,186, or very close to zero. That seems very unlikely.

(The median can never be more than twice the mean; in this case it is
173 percent of the mean. Highly unlikely. )

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