$\begin{align}  & \text{Convert }{{1214}_{5}}\text{ to decimal} \\ & \text{121}{{\text{4}}_{5}}=1\times {{5}^{3}}+2\times {{5}^{2}}+1\times {{5}^{1}}+4\times {{5}^{0}} \\ & \text{121}{{\text{4}}_{5}}=125+50+5+4={{184}_{10}} \\ & Average=\frac{184}{4}=46 \\ & 5\overline{\left){\begin{align}  & 46 \\ & 9\to 1 \\ & 1\to 4 \\ & 0\to 1 \\\end{align}}\right.} \\ & \text{The average of the numbers in base 5 is }{{141}_{5}} \\\end{align}$