CAUTION: This formula will count anything that is a number. If you column has more than dates and those entries are a number, this formula will count them as well.

=COUNTIF(A:A,">1/1/1900")

In cell B1:

=(A1>=$C$1)*(A1<=$D$1)*(CELL("format";A1)="D1")

copied down to B10 and then =SUM(B1:B10)

where C1 is the earliest allowed date and D1 the latest allowed date.
Please note that the last "D1" is not a cell reference but a format code.

Thank you for your help. Unfortunately I don't understand much about formulas in Excel, and so I don't think that I can use yours. Please see the image below. The formula would go in one of the blank cells at the bottom of each column.

Attached Images

Excel example.jpg (139.7 KB, 41 views)

Thank you for your help. That formula works except I forgot to say that row A has a word in it, and I have 17 rows. Could your formula somehow be changed to eliminate row A in the count? Please see the image in the next post.

OP can as well use
To get the formula to work for other columns it's enough to drag the formula right (right.clickinf on right lower corner of cell so that a cross is shown there, and then dragging ro right holding mouse tab down. And after that clearing the formula from abundant cells.

Didn't understand a thing about column A having a word in it? Do you mean column header? Or do dates in column A have some text before or after date? Or is in some cells a text instead of date?

And generally it is bad practice to have any summaries at bottom of data! You may have a situation where you must edit formulas whenever you add new row of data into table. Much better is have for any totals rows reserved at top of table. Additional bonus will be to use Freeze Panes feature to be Totals always displayed.