TI stat summations and guard digits Message #4 Posted by Karl Schneider on 30 Dec 2007, 4:13 p.m., in response to message #3 by Palmer O. Hanson, Jr.
Hi again, Palmer 
Happy holidays, and we all hope that your wife's surgery and recovery turns out for the best.
Quote:
My recollection is that the TI55II displays eight digits but carries eleven digits internally.
Yes, I'm sure that you're correct, and those three extra guard digits contain the small inaccuracy from recalculation of the mean. However, it's possible for those calculations to be exact if the data are entered in ascending or descending order: {4, 5, 6, 7, 8} or {8, 7, 6, 5, 4}. The only intermediate mean average of up to five input data that is not exactly representable using two or fewer decimal points, is the mean of three data having an odd sum.
On a TI55II or similar, try entering {4, 6, 7, 8, 5} using stat summation, or manually calculate
(((4 + 6 + 7)/3)*3 + 8 + 5)/5  6.
I get 1E09 on my LED TI30, which also has an eightdigit mantissa and three guard digits.
Reducing the possibility of overflow with an eightdigit mantissa was probably the reason for the TI55II's statisticalsummation methods. The guard digits were not to be considered reliable; on the LED TI30, they certainly weren't:
http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv016.cgi?read=107358#107358
 KS
Edited: 31 Dec 2007, 2:33 a.m.
