Mean weight of 25 students = 52 kg
Sum of the weights of 25 students = (5225) kg = 1300 kg
Mean weight of the first 13 students = 48 kg
Sum of the weights of the first 13 students = (4813) kg = 624 kg
Mean weight of the last 13 students = 55 kg
Sum of the weights of the last 13 students = (5513) kg =715 kg
Weight of the 13th student = (Sum of the weights of the first 13 students + Sum of the weights of the last 13 students) Sum of the weights of 25 students
= [(624+715)1300] kg
= 39 kg
Therefore, the weight of the 13th student is 39 kg.