To find the average of four numbers, we divide their sum by the total number of numbers. In this case, the sum is \(1214_5\) and there are four numbers.

Let's first convert \(1214_5\) to base 10 to perform the calculation:

\[1214_5 = 1 \cdot 5^3 + 2 \cdot 5^2 + 1 \cdot 5^1 + 4 \cdot 5^0 = 125 + 50 + 5 + 4 = 184.\)

Now, divide the sum by the total number of numbers (which is 4):

Average = \(\frac{184}{4} = 46.\)

Now, let's convert the average back to base 5:

We want to express 46 in base 5.

Divide 46 by 5:

\[

\begin{align}

46 \div 5 &= 9 \, \text{remainder} \, 1 \\

9 \div 5 &= 1 \, \text{remainder} \, 4 \\

1 \div 5 &= 0 \, \text{remainder} \, 1 \\

\end{align}

\)

Reading the remainders in reverse order, we get \(141_5\).