I don't know what statistic you're citing, but those numbers were much, much higher in urban areas. As early as World War I, high school graduation numbers among blacks skyrocketed, as the older generations pushed for their youth - especially the girls - to go to school and get an education.
Three of my four grandparents are high school graduates - the fourth, my paternal grandfather, became a master carpenter; both of my grandmothers are college graduates. If you talk to many, those graduation rates will increase dramatically prior to Depression, then taper off again, but increasing dramatically once again during the second World War.
As I said, the higher rates were in cities. In the country, the emphasis may have been there, but it may not have been pushed as much, with youngsters choosing to become farmers or tradesmen.