Re: uncertainties, PROGRAMMING

[Tim Folkerts <Tim.Folkerts@valpo.edu>]

On Sat, 07 Mar 1998 10:50:38 -0400 (EDT) LUDWIK KOWALSKI 
<KOWALSKIL@alpha.montclair.edu> wrote:

> What would be involved in trying to get such an outcome with 
> a  spreadsheet? 
>
>    bin   1  freq=     0  A= 13    to  13.2
>    bin   2  freq=     0  A= 13.2  to  13.4 
>    bin   3  freq=  2946  A= 13.4  to  13.6  A=area, never below 13.44
>    bin   4  freq= 11818  A= 13.6  to  13.8 
>    bin   5  freq= 20827  A= 13.8  to  14 
>    bin   6  freq= 30062  A= 14    to  14.2 
>    bin   7  freq= 38694  A= 14.2  to  14.4 
>    bin   8  freq= 47444  A= 14.4  to  14.6 
>    bin   9  freq= 50130  A= 14.6  to  14.8 
>    bin  10  freq= 50269  A= 14.8  to  15 
>    bin  11  freq= 49817  A= 15    to  15.2 
>    bin  12  freq= 49634  A= 15.2  to  15.4 
>    bin  13  freq= 44230  A= 15.4  to  15.6 
>    bin  14  freq= 36420  A= 15.6  to  15.8 
>    bin  15  freq= 28679  A= 15.8  to  16 
>    bin  16  freq= 20762  A= 16    to  16.2 
>    bin  17  freq= 12902  A= 16.2  to  16.4 
>    bin  18  freq=  5208  A= 16.4  to  16.6 
>    bin  19  freq=   158  A= 16.6  to  16.8  never above 16.64
>    bin  20  freq=     0  A= 16.8  to  17 

  
Across the top (ROW 1, COLUMNS B...), put n different values of length.
Down one side (Column A, ROWS 2... ), put n different values of width.  
Write one equation to multiple L x W:  +B$1*$A2.  
Copy it to the remaining cells in the n x n region.

This gives a set of possible values for A.  you can either put them 
into bins by hand or use a built-in function to count them up (Excel 
has such a "histogram" function, and I'm sure most others do, too).

I made a 40x40 square with evenly spaced values for L & W  (4.81, 
4.83, ... 5.19; 2.81 ... 3.19). The results I got with 1600 
calculations are are basically indistinguishable from the 500,000 
random calculations.  (Of course, you could easily modify the BASIC 
program to take even steps for L & W and calculate A this same way).
 


13	 13.2		0
13.2	 13.4		0
13.4	 13.6		9
13.6	 13.8		38
13.8	 14.0		68
14	 14.2		96	
14.2	 14.4		124
14.4	 14.6		151
14.6	 14.8		160
14.8	 15.0		162
15	 15.2		159
15.2	 15.4	 	159
15.4	 15.6	 	141
15.6	 15.8 		118
15.8	 16.0 		91
16	 16.2 		65	
16.2	 16.4 		42
16.4	 16.6 		17
16.6	 16.8		0


I imagine it takes about the same time either way  :)






---   Tim Folkerts


********************************************************
Timothy J. Folkerts               Tim.Folkerts@valpo.edu
Dept. of Physics & Astronomy      219-464-6634
Valparaiso University
Valparaiso, IN  46383