## Monday, October 14, 2013

### Central Limit Rabbits

A cute video illustrating the Central Limit Theorem in a "Creature Cast" by animator Shuyi Chiou via the New York Times. Here a normal distribution is presented correctly. On the horizontal axis is a number line of the weight of rabbits. Small rabbits are on the left and large rabbits are on the right. A smooth curve of their relative frequency of occurrence is also shown. The curve is low on each end indicating that at each extreme there are few small rabbits and few large ones. The curve is high in the middle where the relative frequency of average weight rabbits is large. In this case, the population distribution of rabbit weights appears to follow a normal curve. In previous posts, we have seen this number line aspect of such a normal curve indicated correctly and also incorrectly.

In illustrating the Central Limit Theorem the animation goes on to examine the average weight of groups or samples of rabbits.
Such average weights of samples builds up the sampling distribution of these averages. The Central Limit Theorem tells us that these group averages will more closely follow a normal distribution as the group size increases. An illustration starting with the bi-modal distribution of dragon wings is also shown.