- #1

Erland

Science Advisor

- 738

- 136

## Main Question or Discussion Point

Why are so many phenomena well described by the normal distribution?

For example: the height of 18 year old males in Sweden, the weight of apples on a particular tree, the volume of coke cans (supposed to be 33 cl), etc. etc. are all well described by the normal distribution.

How come?

A typical answer would be to refer to the Central Limit Theorem (CLT). In its standard formulation, CLT says that the distribution of the (normalized) average of n indepedent, identically distributed stochastic variables approaches the standard normal distribution as n → ∞.

Although there are several versions of CLT for which the assumptions are weakened, I still don't see how it can be applied to the cases above. Since these don't deal with averages, how can CLT in any form be applied?

For example: the height of 18 year old males in Sweden, the weight of apples on a particular tree, the volume of coke cans (supposed to be 33 cl), etc. etc. are all well described by the normal distribution.

How come?

A typical answer would be to refer to the Central Limit Theorem (CLT). In its standard formulation, CLT says that the distribution of the (normalized) average of n indepedent, identically distributed stochastic variables approaches the standard normal distribution as n → ∞.

Although there are several versions of CLT for which the assumptions are weakened, I still don't see how it can be applied to the cases above. Since these don't deal with averages, how can CLT in any form be applied?