Answer: $1.\dot{6}$ or $\frac53$ or $1\frac23$


Decimals
The mean is $(1.\dot{2}+2.\dot{1})\div2=3.\dot{3}\div2=1.\dot{6}$


Fractions
$1.\dot2 = 1\frac29$

$2.\dot1 = 2\frac19$

$1\frac29+2\frac19=3\frac39=3\frac13$

$3\frac13\div2=1\frac12+\frac16=1\frac23$