The mean weight of 25 students of a class is 52 kg. If the mean weight of the first 13 students of the class is 48 kg and that of the last 13 students is 55 kg, find the weight of the 13th student.
Mean weight of 25 students $=52 \mathrm{~kg}$
Sum of the weights of $25 \mathrm{students}=(52 \times 25) \mathrm{kg}=1300 \mathrm{~kg}$
Mean weight of the first 13 students $=48 \mathrm{~kg}$
Sum of the weights of the first $13 \mathrm{students}=(48 \times 13) \mathrm{kg}=624 \mathrm{~kg}$
Mean weight of the last 13 students $=55 \mathrm{~kg}$
Sum of the weights of the last $13 \mathrm{students}=(55 \times 13) \mathrm{kg}=715 \mathrm{~kg}$
Weight of the 13 th 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
$=[(624+715)-1300] \mathrm{kg}$
$=39 \mathrm{~kg}$
Therefore, the weight of the 13 th student is $39 \mathrm{~kg}$.