The average weight of a group of 15 students is 70 kg. Five more students of weight 65 kg, 68 kg, 45 kg, 77 kg and 62 kg join the group. What is the change in the average weight (rounded off to the nearest integer) of the group?

Let's find the total deviation from the initial average of 70 kg for the 5 new students: Deviation of 65 kg = $65-70=-5$ Deviation of 68 kg = $68-70=-2$ Deviation of 45 kg = $45-70=-25$ Deviation of 77 kg = $77-70=+7$ Deviation of 62 kg = $62-70=-8$ Total deviation = $(-5)+(-2)+(-25)+7+(-8)=-33\text{ kg}$ This total deviation is distributed over the new total number of students ($15+5=20$):
$$\text{Average change}=\frac{-33}{20}=-1.65\text{ kg}$$
Rounding off $-1.65\text{ kg}$ to the nearest integer gives $-2\text{ kg}$, which means the average weight decreases by 2 kg.