Step 1: Understand the quantity.
We need the average (mean) depth of all the oceans of the world taken together.
Step 2: Recall the standard figure.
The commonly accepted average ocean depth is close to 3.7 km, found by dividing total water volume by total ocean area.
Step 3: Compare with the choices.
The options 3.655, 3.566, 3.866 and 3.688 km are all near this value, so we need the most precise one.
Step 4: Pick the closest standard value.
The accepted mean depth used in textbooks is about 3.688 km.
Step 5: Confirm it is reasonable.
This is far deeper than the average height of land above sea level, which agrees with how vast and deep the oceans are.
Step 6: State the answer.
So the average depth of the world's oceans is about 3.688 km.
\[ \boxed{3.688 \text{ km}} \]