Even number between 11 to 63 = 12, 14, 16, .......60, 62.

This is a series of consecutive even numbers

According to the formula,

The average of consecutive numbers=$\frac{\mathrm{First} \mathrm{number}+\mathrm{Last} \mathrm{number}}{2}$

$$\begin{gathered} =\frac{12+62}{2} \\ =\frac{74}{2} \\ =37 \end{gathered}$$

Hence, Option D is correct.