I have $10$ balls which are numbered from $1$ to $10$. Randomly select (uniform) these balls into two groups (number of balls in two groups is different). Then compute the mean value of numbers on these balls $$m_i=\frac {\text{total number on balls in group $i$}}{\text{total balls in group $i$}}$$ At the fist trial, I saw that $m_1=m_2$. Then I mixed these balls and classified again into two groups. Note that, the number balls in each group of this trials may be same or different will first trial.
At this trail, I saw that $m_1$ still equals $m_2$. At that sense, Could I conclude that these balls in two group are similar in two trials?