2010 At the 2010 census Big River had a population of 1,327. The population density was . The racial makeup of Big River was 1,137 (85.7%) White (79.5% Non-Hispanic White), 14 (1.1%) African American, 50 (3.8%) Native American, 2 (0.2%) Asian, 0 (0.0%) Pacific Islander, 54 (4.1%) from other races, and 70 (5.3%) from two or more races. Hispanic or Latino of any race were 160 people (12.1%).
2010 At the 2010 census Big River had a population of 1,327. The population density was . The racial makeup of Big River was 1,137 (85.7%) White (79.5% Non-Hispanic White), 14 (1.1%) African American, 50 (3.8%) Native American, 2 (0.2%) Asian, 0 (0.0%) Pacific Islander, 54 (4.1%) from other races, and 70 (5.3%) from two or more races. Hispanic or Latino of any race were 160 people (12.1%).