Find last row and count multiple criteria using last row (bottom up) for results

I'm not up on VBA as of yet, so I'm looking for a formula that will generate my results for right now.

Need formula where I can set my search within a set RANGE (A1:A5000, BA1:BA5000) (DID THIS SO THAT I DON’T HAVE TO MANUALLY CHANGE FORMULA EACH TIME REPORT IS RUN… ANTICIPATING FUTURE GROWTH) and fills in my Template form

SCENERIO: ADHOC report were the columns remain constant and COLUMN A will always have data present.
1) Use the range, but FIND the LAST ROW within the range to determine end of record dependent on Column A (always has data).
EX: RANGE SET AS (A1:A5000, BA1:BA5000), BUT the last row (last student record) in my spreadsheet is 3935 (currently) not 5000 (future growth).

2) Once LAST ROW identified within RANGE, I need to COUNT Multiply criteria from Column AZ and BA

To add up the multiple criteria for Ethnicity NHS (stands for Non-Hispanic) + Race Asian (AN) + Race Blank ('=') = Asian count. This formula also works, but would like to insert a condition that will find the LAST ROW to ensure the count stops
=SUM(COUNTIFS('Census 2012'!$AZ$2:$AZ$5000,"NHS",'Census 2012'!$BA$2:$BA$5000,"AN")+ COUNTIFS('Census 2012'!$BA$2:BA$5000,"AN",'Census 2012'!$AZ$2:$AZ$5000,"="))


To add up the multiple criteria for Ethnicity HIS (stand for Hispanic) + Race Asian (AN) = Hispanic count. This formula also works, again condition to find LAST ROW
=SUM(COUNTIFS('Census 2012'!BA2:BA5000,{"AN","AS","BL","HP","WH","="}, 'Census 2012'!AZ2:AZ5000,"HIS"))


3) To add up the multiply criteria for Ethnicity NHS (stands for Non-Hispanic) is "BLANK" + Race is "BLANK" = Unknown count
Because students don’t always answer all the required data on their online application, these fields appear as BLANK CELLS when data is retrieved in the ADHOC report. I used the following formula for the time being and it works, but I would have to verify last record and change the End of Record range AZ:_____ each time to match. If I didn’t use this current formula, it would keep counting until record BA5000 throwing off my actual count. This field is my Unknown student population.
=COUNTIFS('Census 2012'!AZ2:AZ3935,"",'Census 2012'!BA2:BA3935,"")


Sorry for the length of the inquiry, but I wanted to be as detailed as possible to explain my situation and alleviate back and forth questions. I'm on a deadline to create our FACTBOOK and I refuse to manually look this data up by creating multiple Pivot tables to get my data. Do you have any suggestions (a formula) that will read LAST ROW and return a count using my criteria?

Your expertise is most appreciated!!! Thx in advance. Cris

Thx oeldere, but I'm not looking for Pivot tables... I use them already to get such data.

I'm looking for a formula that will go to the LAST ROW based on COLUMN A and use the LAST ROW as my "End of Record" identifier and use the LAST ROW found and go COLUMN BA to calculate from LAST ROW bottom/up and count the number of "Blank cells" to give me my UNKNOWN students. I as stated, my COUNTIFS work, but I must manually adjust the formula and insert the LAST ROW from a visual lookup and change the range. This is what I'm trying to alliviate.

The concept like what INDEX will do, but I'm not wanting to know the LAST ROW NUMBER, just want to use the idea of finding the LAST ROW and possibly do a COUNTIF for COLUMN BA. How to combine the two???

=INDEX(Sheet1!A2:A5000,MATCH(1E+100,Sheet1!A2:A5000))