I am sure you can do this with script and using the info in this post you might be able to do it without:
How To Use Longitude/Latitude with Address Fields.https://community.quickbase.com/quickbase/topics/how-to-use-longitude-latitude-with-address-fieldsIn either case you will need a table mapping each state to the centroid latitude and longitude:
State,Lat,Lon
Alabama,32.7794,-86.8287
Alaska,64.0685,-152.2782
Arizona,34.2744,-111.6602
Arkansas,34.8938,-92.4426
California,37.1841,-119.4696
Colorado,38.9972,-105.5478
Connecticut,41.6219,-72.7273
Delaware,38.9896,-75.505
District of Columbia,38.9101,-77.0147
Florida,28.6305,-82.4497
Georgia,32.6415,-83.4426
Hawaii,20.2927,-156.3737
Idaho,44.3509,-114.613
Illinois,40.0417,-89.1965
Indiana,39.8942,-86.2816
Iowa,42.0751,-93.496
Kansas,38.4937,-98.3804
Kentucky,37.5347,-85.3021
Louisiana,31.0689,-91.9968
Maine,45.3695,-69.2428
Maryland,39.055,-76.7909
Massachusetts,42.2596,-71.8083
Michigan,44.3467,-85.4102
Minnesota,46.2807,-94.3053
Mississippi,32.7364,-89.6678
Missouri,38.3566,-92.458
Montana,47.0527,-109.6333
Nebraska,41.5378,-99.7951
Nevada,39.3289,-116.6312
New Hampshire,43.6805,-71.5811
New Jersey,40.1907,-74.6728
New Mexico,34.4071,-106.1126
New York,42.9538,-75.5268
North Carolina,35.5557,-79.3877
North Dakota,47.4501,-100.4659
Ohio,40.2862,-82.7937
Oklahoma,35.5889,-97.4943
Oregon,43.9336,-120.5583
Pennsylvania,40.8781,-77.7996
Rhode Island,41.6762,-71.5562
South Carolina,33.9169,-80.8964
South Dakota,44.4443,-100.2263
Tennessee,35.858,-86.3505
Texas,31.4757,-99.3312
Utah,39.3055,-111.6703
Vermont,44.0687,-72.6658
Virginia,37.5215,-78.8537
Washington,47.3826,-120.4472
West Virginia,38.6409,-80.6227
Wisconsin,44.6243,-89.9941
Wyoming,42.9957,-107.5512
I obtained this data by following the info in this wikipedia article:
List of geographic centers of the United Statesthe center for a state was found by suspending a cardboard cutout of the state by a string, and then drawing a vertical line from the suspension point. After rotating the cutout 90 degrees and drawing another vertical line from the new suspension point, the intersection of the two vertical lines was used as the geographic center.https://en.wikipedia.org/wiki/List_of_geographic_centers_of_the_United_StatesIf you need additional ask away.