A couple of issues...

1) It doesn't take into consideration ties for 10th place.

2) Owing to the MODE function, #N/A is returned when values occurring
more than once have been exhausted and only values occurring once remain.

Nevertheless, very interesting Harlan!

In article . com,
"Harlan Grove" wrote:

Ancillary cells aren't necessary.

B2 [array formula]:
=INDEX($A$2:$A$100,MODE(MATCH($A$2:$A$100,$A$2:$A$ 100,0)))

B3 [array formula]:
=INDEX($A$2:$A$100,MODE(IF(COUNTIF(B$2:B2,$A$2:$A$ 100)=0,
MATCH($A$2:$A$100,$A$2:$A$100,0))))

Fill B3 down into B4:B11.