- #1
carllacan
- 274
- 3
Why are there so many physical processes which are described (with more or less accuracy) by a normal distribution?
D H said:A more nefarious reason: It's easy. The normal distribution is extremely amenable to analysis. People oftentimes use a normal distribution when they shouldn't be doing that. I myself have been committed that statistical crime.
Filip Larsen said:The short answer is, that it is due to the Central Limit Theorem [1].
[1] http://en.wikipedia.org/wiki/Central_limit_theorem
carllacan said:I'm reading on the CLT and I'm getting more and more confused. I'm getting the idea that according to it every physical experiment would end up giving a normal distribution, but that is obviously false. Can someone clear my head?
Very interesting. And why is it that the normal distribution has the most entropy?
carllacan said:And why is it that the normal distribution has the most entropy?
Stephen Tashi said:"Normal distribution" refers to a family of distributions and not all members of that family have the same entropy. Is isn't clear what you mean by "the" normal distribution.
carllacan said:Why are there so many physical processes which are described (with more or less accuracy) by a normal distribution?
Is there a "proof" that the normal distribution is, in fact, the binomial distribution as n approaches infinity?
If so, that would explain a lot.
Normal distributions, also known as Gaussian distributions, are used frequently in statistics because they accurately describe many real-world phenomena. This is due to the central limit theorem, which states that the sum of a large number of independent and identically distributed random variables will tend towards a normal distribution.
One of the main reasons normal distributions are considered special is because they have a symmetric bell-shaped curve, with the mean, median, and mode all being equal. This makes them easy to understand and work with in statistical analyses.
The normal distribution is often used to represent the concept of "average" because it is the most common distribution for values to fall around a central value. This central value is represented by the mean of the distribution, making it a useful measure of central tendency.
No, not all data points in a normal distribution are truly "normal". In fact, some data points may deviate significantly from the mean, especially in larger datasets. However, the majority of the data will still fall within a few standard deviations of the mean, making the distribution appear normal.
Yes, it is possible for a dataset to have more than one normal distribution. This typically occurs when there are distinct subgroups within the dataset that follow different normal distributions. In this case, it may be more appropriate to analyze each subgroup separately to get a more accurate representation of the data.