My Final #DIV/0! that I'd like to say Goodbye to!

[Harlan Grove]

I find it very hard to believe that Excel which is designed to handle huge
volumes, would not take advantage of simply keeping the results from one
function call to use in another identical function call. . . .

Get used to it.

Excel formulas represent a simple interpreted language, with the stress on
SIMPLE. You can test this for yourself by using macros to repeatedly
recalculate ranges containing formulas like

=COUNT(DATA)+COUNT(DATA)

vs

=2*COUNT(DATA)

But if you believe I'm wrong about this, then just wait a few minutes for
someone else to show how I'm wrong about this. Just don't hold your breath.

. . . BTW, your formula does not catch the presence of logical values
which should not be there if range is supposed to be numerics or blanks.

Fine.

=IF(COUNT(MATCH({"?*",TRUE,FALSE},DATA,0)),"invalid entries",
IF(COUNT(DATA),AVERAGE(DATA),""))

And also why use "?*" when "*" should do.

....

Because I was making my formula mimick yours.

As I've already tried to point out to you, COUNTBLANK(DATA) includes not
only truly blank cells (those for which ISBLANK returns TRUE) but also cells
evaluating to "" in its result. Matching "*" would treat cells evaluating to
"" as invalid, so UNLIKE your formula, whereas matching "?*" will match TEXT
containing ONE OR MORE characters.

If YOU want to restrict DATA to contain only numbers and truly blank cells,
you need to use either

COUNT(DATA)=COUNTA(DATA)

or

COUNT(DATA)+COUNTIF(DATA,"=")=ROWS(DATA)

but note that the latter requires that DATA span a single column.