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.

Sherlock Holmes quotes Sherlock Holmes crediting a Great Statistician

The TV series Elementary is a modern take on Arthur Conan Doyle's detective Sherlock Holmes. In the latest episode "M.", Sherlock Holmes played by Jonny Lee Miller quotes Sherlock Holmes from chapter 10  "The Sign of the Four," saying:

while the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.

He could be talking about the Law of Large Numbers or perhaps the Central Limit Theorem or, even more simply, any random variable with its individual values and its given probability distribution of the aggregate of its values.

In the book, Arthur Conan Doyle has Holmes reference the 19th century British philosopher, explorer Winwood Reade who wrote in his book The Martyrdom of Man:

All the events which occur upon the earth result from law: even those actions which are entirely dependent on the caprices of the memory or the impulse of the passions are shown by statistics to be, when taken in the gross entirely independent of the human will. As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.

In the TV show, Holmes credits a "great statistician".
I like that.