I've just had a look at the |STAT source, and it computes the variance with

        double  M       = Sum/N;                /* mean */
        double  var     = (s2 - M*Sum)/(N-1);   /* variance */

where s2 is the sum of squares. In most reasonable situations, this approach will work fine. It just doesn't take as wide a variety of inputs as is easily possible to achieve with normal floating point doubles. In fairness, the |STAT terms and conditions state:

|STAT PROGRAMS HAVE NOT BEEN VALIDATED FOR LARGE DATASETS, HIGHLY VARIABLE DATA, NOR VERY LARGE NUMBERS.