2015-I-12

$\begin{array}{cl}=& {\displaystyle \frac{40+42+\dots +79}{20}}\\ =& 55\text{ kg}\end{array}$

The median

$\begin{array}{cl}=& {\displaystyle \frac{52+52}{2}}\\ =& 52\text{ kg}\end{array}$

The range

$\begin{array}{cl}=& 79–40\\ =& 39\text{ kg}\end{array}$

Suppose one of the new comers weighs $39\text{ kg}$. For the mean is increased by $1\text{ kg}$,

$\begin{array}{rcl}{\displaystyle \frac{1100+39+x}{22}}& =& 56\\ x& =& 93\end{array}$

However, the new range becomes $53\text{ kg}$, not $40\text{ kg}$. Hence, this case is rejected.

Suppose one of the new comers weighs $80\text{ kg}$. For the mean is increased by $1\text{ kg}$,

$\begin{array}{rcl}{\displaystyle \frac{1100+80+x}{22}}& =& 56\\ x& =& 52\end{array}$

Hence, the weights of the two students are $52\text{ kg}$ and $80\text{ kg}$.