Numeric Formatting Issue

[BertieDark]

I have noticed a discrepancy when applying a format to a mean where the last digit is 5. In the example below two means are calculated, both giving a result of exactly 90.55. However when the results are formatted to 6.1, one mean shows as 90.5 and the other as 90.6.

data problem;
	input gp x;
	datalines;
	1 92.8
	1 93.4
	1 94.6
	1 81.4
	2 90.55
	2 90.55
	2 90.55
	2 90.55
	;
run;
proc means data=problem mean;
	by gp;
	var x;
	output out=means mean=x;
run;
proc print data=means; 
	format x 6.1;
run;

The output from this code is as follows:

--------------------------------------------- gp=1 ---------------------------------------------

                                      The MEANS Procedure

                                     Analysis Variable : x

                                                  Mean
                                            90.5500000

--------------------------------------------- gp=2 ---------------------------------------------

                                     Analysis Variable : x

                                                  Mean
                                            90.5500000

                            Obs    gp    _TYPE_    _FREQ_         x

                             1      1       0         4        90.5
                             2      2       0         4        90.6

Can anyone explain this please?

[PaigeMiller · Accepted solution]

This is due to rounding error, which happens when computing means and when changing the number of decimal places. This is usually unavoidable when working with fractions/decimals that are not a negative power of 2, or multiples thereof.

If you change the format of X to best32., you will see 

gp                                   x

 1                    90.5499999999999
 2                               90.55

and so to round to one decimal place, x for gp=1 is 90.5, while for gp=2 rounded to one decimal place x is 90.6.

If you really don't want this to happen, and you need x to one decimal place without this rounding error, you can first run this and then to one decimal place you get the same answer.

data means;
    set means;
    x=round(x,0.01);
run; 

[BertieDark]

Thank you @PaigeMiller