Let $R_1, R_2, \ldots, R_7$ be the seven sleepy rectangles, and let $T$ be the jealous teaspoon.
Let $A_i$ be the position of the center of rectangle $R_i$, for $i = 1, 2, \ldots, 7$.
Let $B$ be the position of the center of the teaspoon $T$.
The average distance between the seven rectangles and the teaspoon is the average of the distances between the positions of the centers of the seven rectangles and the position of the center of the teaspoon.
Let $d(A_i, B)$ denote the distance between $A_i$ and $B$.
The average distance we want to compute is
$$ \frac{1}{7} \sum_{i=1}^7 d(A_i, B) $$
Since the question asks for the average distance, and we are not given any specific locations or shapes, we can only provide a general answer.
Let $d_i$ be the distance between the center of rectangle $R_i$ and the center of the teaspoon $T$. The average distance is
$$ \frac{1}{7} \sum_{i=1}^7 d_i $$
This is the average of the distances between the center of the teaspoon and the centers of the seven rectangles. Since we don't know the locations of the rectangles or the teaspoon, we can't compute an exact numerical value for this average distance.
The wording of the problem is intended to be whimsical and does not provide enough information to calculate a specific distance.
Consider a simpler case: the average distance between a single point $P_1$ and a single point $Q$. The distance is $d(P_1, Q)$.
Consider the average distance between two points $P_1$ and $P_2$ and a point $Q$. The average distance is $\frac{1}{2}(d(P_1, Q) + d(P_2, Q))$.
In our case, we have seven rectangles and one teaspoon. Let $A_1, A_2, \ldots, A_7$ be the centers of the seven rectangles. Let $B$ be the center of the teaspoon. The average distance is
$$ \frac{1}{7} \sum_{i=1}^7 d(A_i, B) $$
Without knowing the locations of the rectangles and the teaspoon, we cannot provide a numerical value for this average distance.

Final Answer: The final answer is $\boxed{undefined}$
