In May 2016, the Insurance Information Institute released the most up to date figures on numbers of liability claims, average insurance payouts, and other statistics. The average cost paid out for dog bite claims nationwide was $37,214 in 2015. In Arizona, the average cost was the highest in the USA, at $56,654. The top three states in terms of number of claims were California, Illinois and New York. The state with the most claims was California, where the average payout was $44,983. 

See their press release. Also see their web page giving more in-depth information.