Since no one scored Zero your distribution of scores is bi-modal.  with the
mode being 50 and 51.  Also, your n is 2550, not 2500.  Your distribution
is kind of like a triangle with a flat top.
Phyllis

At 08:43 AM 2/27/2003 -0500, you wrote:
>I guess at a University, I shouldn't have been surprised at the plethora
>of responses I got to my statistics question. But, given the paucity of my
>ability to anticipate this, I was. And the variance of responses was
>clearly significant at some level of something. This morning an esteemed
>colleague in the physics dept. asked for a review of the literature.
>
>In lieu of that, I am going to attempt to break down the problem, at least
>as my feeble, over-achieving and underpaid mind calculated it (although
>one writer did point out the 100 should be eliminated to round out the
>distribution. I had thought about that, too since no one scored 0). But
>this is close enough for government work, so to keep it simple, I'm
>sticking to the 1-100 scenario.
>
>First the question of n (unless, of course, we consider the class a
>population rather than a sample, in which case we would respectfully refer
>to them as N. I guess in that case I should at least make them graduate
>students).
>
>
>
>1+2+3+4+5+6+7+8+9+10=55
>
>11+ ....20=155
>
>21+ ...30=255
>
>31+ ...40=355
>
>41+ ...49=405
>
>Total = 1225 x 2 + 50 = 2500
>
>OK, my original N of 2468 was wrong. I went to Georgia, not Georgia Tech!!
>I'll be glad to write an essay giving a subjective, even phenomenological
>account of the experience.
>
>So, 40 thru 49 = 455
>
>and 51 thru 60 = 455
>
>giving us 910
>
>then the ever present but mediocre mean, median, and modal 50 who scored a
>50 brings the 40 - 60 group to 960.
>
>
>Now granted I cut my share of 100-level math classes, thus amazing even
>myself by getting thru four doctoral level statistics and research design
>courses, but I don't believe 960 is anywhere like 68% of the 2500
>well-distributed (graduate) students that took the test.
>
>However, among the widely variant responses (including another esteemed
>colleague in psychology who pointed out that my fundamental error was that
>such a distribution is a triangular one rather than the bell-shaped normal
>distribution, hence not applicable) was the following:
>
><<Out of 2550 students, 1,741 (or 68.26% students) scored between 40 and 60.>
>
>So, something definitely ain't Cartesian here!!!
>
>Comments?
>
>Thanks,
>
>ED
>
>
>
>
>
>
>
>
>
>
>W. Ed Smith, Ph.D.
>Psychologist and Clinical Services Coordinator
>Counseling and Career Planning Center
>University of Tennessee at Chattanooga
>615 McCallie Ave.
>Chattanooga, TN  37403
>
>423 425-4438
>
>
>Email communication cannot be considered confidential, and may not meet
>the legal requirements of Tennessee for privileged communication.