Hi Brian,
While Numbers 3 doesn't support categories, it's still possible (fairly easy, actually) to get category totals or counts. You'll want to do this on a separate table.
Here's an example, using the same categories as above in column B, but with some data aded in column C. The data table is named "Data," the summary table, reporting the count and total for each category, in named Summary. For ease of in head calculations, the 'amount' for every entry in a category is the position of that letter in the alphabet, making the total count x 1 for a, count x 2 for b, etc.

Data has no formulas. All data shown (categories and amounts) can be considered as directly entered from the keyboard, or pasted in from another source.
Summary has two formulas, one to count the number of entries in each category, the other to total the amount entered in each category. The category list is entered directly in column A. Categories must be exact matches of those in column B of Data.
Summary::B2: =COUNTIF(Data :: $B,A)
English: Count all of the entries in Data, Column B that match the entry in this row of Column A of this table.
Fill this formula down from B2 (of Summary) to the last row of the table.
Summary::C2: =SUMIF(Data :: $B,A,Data :: $C)
English: Check the category data in column B of Data. If the category on a row matches the value in this row of column A of this table, include the value in that row of column C of Data in the total calculated on this row.
Fill this formula down from Summary::C2 to the last row of column C of this table.
NOTE that the calculations do not depend on the table being sorted into any particular order.
For another example, open a new document from the Personal Budget template included with Numbers, and examine the category totals calculations in that document.
Regards,
Barry