The Mean and SD are set by Daigian's position. Your options are therefore not possible... - Edit 1
Before modification by Shannow at 02/11/2012 07:50:14 AM
And Egwene is nearly 2x Moiraine. This is essentially a theory I put forth several years ago. I started with Daigian being. 16, other than that it's pretty much identical.
Edit: and does you Math work downward toward Morgase for 6SD? There are several women in those levels as well and we know there must be as many SD between Mean and Morgase as there are between Lanfear and Morgase. Your SD is too large for the Mean to located at 16.6 and allow for a 0 or 1 minimum. It works better when you have Daigian at a 16, Mean around 24 and Egwene 80 meaning 4SDs with the a forsaken all falling at various places in the 5th SD.
On the reverse side this still doesn't work as the SD you've calculated is too large for a Mean so low. Here is the problem, on a fixed scale measuring Lanfear to Morgase with 6 SD the spread of each SD will be 16.5. This is based on your math above with Lanfear at 100 and Morgase at 1. This makes the Mean 3 SD above Morgase and 3 below Lanfear. Roughly 49.5, but still does not work perfectly because Daigian is vastly too weak to be within 1 SD. So we must assume we can ignore that in order to place her with some accuracy, but it needs to be within a reasonable range for her to be accepted. If we place her 2 SDs above Morgase at a level 16.5 that gives us many levels for various AS leading up to the Mean, and still keeps the levels above the mean reasonably populated (especially if we look to New Spring AS and other groups of women)
However, if you accept that Moiraine is at Mean, in this case a 49.5 we can actually make this work. 1 SD up you may find Cadsuane around a 66, 1 SD down you find Verin around a 33. 2 up around an 80 is Egwene and 2 down you have Daigian at 16. 3 up are the Forsaken and 3 down is Morgase.
This squares with other RJ quotes of how the AS cover more levels than we thought and allows for a BC with the same number of Standard Deviations between Morgase and the Mean and Lanfear and the Mean.
Edit: and does you Math work downward toward Morgase for 6SD? There are several women in those levels as well and we know there must be as many SD between Mean and Morgase as there are between Lanfear and Morgase. Your SD is too large for the Mean to located at 16.6 and allow for a 0 or 1 minimum. It works better when you have Daigian at a 16, Mean around 24 and Egwene 80 meaning 4SDs with the a forsaken all falling at various places in the 5th SD.
On the reverse side this still doesn't work as the SD you've calculated is too large for a Mean so low. Here is the problem, on a fixed scale measuring Lanfear to Morgase with 6 SD the spread of each SD will be 16.5. This is based on your math above with Lanfear at 100 and Morgase at 1. This makes the Mean 3 SD above Morgase and 3 below Lanfear. Roughly 49.5, but still does not work perfectly because Daigian is vastly too weak to be within 1 SD. So we must assume we can ignore that in order to place her with some accuracy, but it needs to be within a reasonable range for her to be accepted. If we place her 2 SDs above Morgase at a level 16.5 that gives us many levels for various AS leading up to the Mean, and still keeps the levels above the mean reasonably populated (especially if we look to New Spring AS and other groups of women)
However, if you accept that Moiraine is at Mean, in this case a 49.5 we can actually make this work. 1 SD up you may find Cadsuane around a 66, 1 SD down you find Verin around a 33. 2 up around an 80 is Egwene and 2 down you have Daigian at 16. 3 up are the Forsaken and 3 down is Morgase.
This squares with other RJ quotes of how the AS cover more levels than we thought and allows for a BC with the same number of Standard Deviations between Morgase and the Mean and Lanfear and the Mean.
The fact that Daigian's exact position is confirmed without a doubt makes certain implications unavoidable, thus invalidating most of your suggestions above.
For example.
Daigian IS 0.32 SD from the Mean. That's a fact, based on 37.5% of the population falling below her. That is indisputable. So, if as you suggest, we put Moiraine (who is at least 3 times Daigian's strength) at the Mean, that would mean that the SD is at least 6 times Daigian's strength (2 times Moiraine's strength).
That would mean that a channeler 1 SD above the mean would be 2 times as strong as Moiraine, and a channeler 2 SD above the Mean would be 4 times Moiraine's strength, invalidating the whole reason you put Moiraine at a hypothetical 50.
As I said in my first post, the numbers you assign to an individual are irrelevent. The maths remain the same in assigning proportionate strength to them. Meaning that if you make Daigian a 16 and Moiraine a 50, then it simply means that the strength scale becomes a 1-150 scale, instead of a 1-100 scale.
The fact is that for a normal distribution to apply, given Daigian's position 0.32 standard deviations from the Mean, and given the number of times Moiraine and Egwene are stronger than Daigian, the model HAS to have a Mean relatively close to Daigian's strength level.
The other issue you raised is Egwene. This model is based on the assumption that Egwene lies 3 SD above the Mean. You propose 4 SD as more appropriate.
This does not fit the evidence in the books, because a channeler 4 SD above the Mean would be a 1 in 32000 occurence more or less, using Sidious's quick reference guide above.
Egwene is not close to that level of rarity. We have 10 or more channelers of her strenth just from the 5,000-10,000 Aes Sedai, Aiel, Kin, and Windfinder channelers.
She is a 3 SD level of rarity at most.
I appreciate you making these suggestions, because in answering them, the correctness of the model is simply being confirmed.
Daigian being 0.32 SD below the Mean imposes a bunch of irrefutable restrictions that cannot be circumvented, and which solidifies the relative strength of the channeling population beyond doubt, to be honest.