Dawn,
Griffiths Valuation was a survey of heads of households, between 1848 and 1864. There are a number of Dean families listed. My guess is your great great grandfather wouldn't be listed, but probably his father. You can find more information here:
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&Submit.x=28&Submit.y=20&Submit=Submit&familyname=dean&firstname=&baronyname=&countyname=MAYO&unionname=&parishname=KILFIAN
The tithes, as mentioned above, would be from about 1832.
If you want more information about Kilfian Parish, you can read here:
http://www.rootsweb.ancestry.com/~irlmayo2/kilfian_cp_characteristics.html
Kilfian Parish suffered badly during the Great Hunger of 1846 - 1850:
"Kiflian Civil Parish saw almost a 50% drop in its population between 1841 (6,064) and 1851 (3,348). That number continued to decline and by the year 1911 there were only 1,750 people residing in this Civil Parish."
Finally, you can find some birth and marriage records for Kilfian parish here:
http://www.kilfiancrosskin.com/
Feel free to ask more questions. My ancestors also came from Kilfian.
John