Say I make 3 independent experiments and these are the outputs:
O/P of $1$st exp : $1,2,3$
O/P of $2$nd exp : $4,5,6$
O/P of $3$rd exp : $7,8,9$
In general ${\rm Var}(A+B+C) = {\rm Var}( A ) + {\rm Var}( B ) + {\rm Var}( C )$
In this case ${\rm Var}(\text{1st}) + {\rm Var}(\text{2nd}) + {\rm Var}(\text{3rd}) \ne {\rm Var}(1,2,3,4,5,6,7,8,9)$
Why ?