Regarding the central limit theorem.
The central limit theorem states that when sampling from an independent and identically distributed population, the subgrouped parameters will approach a normal distribution as n->infinity.

Now what if the population follows a function such as:
y = sin(x) + noise
Suppose you are drawing samples from this population, and each consecutive subgroup is drawn exactly one wavelength apart. Furthuremore, the subgroups that are formed are from samples drawn consecutively.
Imagine if each circle in the image posted, is a subgroup of size m.

Would the subgroup parameters still follow a normal distribution?