Put the date you're looking to use as a break point into C1,

Then use this for *before* that date:

=SUMPRODUCT((B2:B10<>"")*(B2:B10<C1))

And this for *after* that date:

=SUMPRODUCT((B2:B10<>"")*(B2:B10>C1))

You realize, that Sam will *not* be counted at all, since he was not born
before *or* after April 1.

To *include* the date in the formula, just add an equal sign:
<=

*BUT* don't add it to *both* formulas, otherwise you'll count Sam *twice*.