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


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