According to the flight crew, they were deviating around known convective activity and anticipated some turbulence. The flight crew stated they selected the fasten seatbelt sign on approximately two minutes prior to the turbulence encounter. The flight was level at FL370 about 80 miles southwest of McCook, Nebraska when they encountered turbulence characterized by the flight crew as severe. FDR data indicated the airplane was level with airspeed of 258 knots, when the airspeed momentarily increased to 268 knots and varied between 268 and 244 knots over the next 10 seconds. There was an approximately 10 second period of fluctuations in both vertical and lateral acceleration. The vertical acceleration fluctuated between -.55 g's to a peak of +1.64 g's while lateral acceleration changed from -.13 g's to +.23 g within three seconds. The flight attendant in the forward jumpseat was making an announcement regarding the seatbelt sign and hit her head on the back of the jumpseat when the flight encountered turbulence. She reported that she saw a passenger in the rear of the cabin thrown against the ceiling and then back down to the floor and another passenger displaced from her seat hit her head on the overhead storage compartments. A passenger in the aft lavatory was thrown against the ceiling and wall and two additional passengers were displaced from their seats. The cabin crew contacted the flight crew to notify them of the injuries, and the flight crew arranged for paramedics to meet the airplane at the destination airport. Three passengers were transported to a local hospital. All were treated and released; one was diagnosed with a dislocated shoulder and a chipped bone.