The mean weight of 120 students of a school is 52.75 kg. If the mean weight of 50 of them is 51 kg, find the mean weight of the remaining students.

Mean weight of 120 students = 52.75 kg

Let a be the sum of weights of 120 students.

Mean weight of 120 students = $\dfrac{\text{Sum of all observations }}{\text{Number of all observations }}$

⇒ 52.75 = $\dfrac{a}{120}$

⇒ a = 120 x 52.75

⇒ a = 6,330

Mean weight of 50 students = 51 kg

Let b be the sum of weights of 50 students.

⇒ 51 = $\dfrac{b}{50}$

⇒ b = 50 x 51

⇒ b = 2,550

Sum of weights of remaining (120 - 50) 70 students = 6,330 - 2,550 = 3,780

Mean weight of remaining 70 students = $\dfrac{3780}{70}$

= 54

Hence, the mean weight of remaining 70 students is 54 kg.