Since I've proven that it's not a normal distribution in units of absolute strength, SDs don't apply - Edit 1
Before modification by Shannow at 17/11/2012 07:55:34 PM
Hi all,
My question is how many standard deviations is Lanfear above the mean? Is she 4, 5, 6, or some other number? According to Wikipedia, http://en.wikipedia.org/wiki/Standard_deviation, (see the chart in the middle of the page) we get the following probabilities:
4 SD = 99.993 666% or in other words, 1 / 15,787
5 SD = 99.999 942 6697% or in other words, 1 / 1,744,278
6 SD = 99.999 999 8027% or in other words, 1 / 506,797,346
Now, if you like round numbers then you might want to use the following (also taken from the same chart on Wikipedia):
1 out of 100,000 = 4.417 173 SD from the mean
1 out of 1,000,000 = 4.891 638 SD from the mean
1 out of 10,000,000 = 5.326 724 SD from the mean.
I don't know if it is possible for us to come to a consensus on where Lanfear is, that is, how many standard deviations is she above the mean. But if we know her level, by extrapolation we can also assign Morgase the exact opposite SD below the mean. Then we can assign Daigian and that should allow us to fill in everybody else.
Any insights are appreciated.
Thanks
My question is how many standard deviations is Lanfear above the mean? Is she 4, 5, 6, or some other number? According to Wikipedia, http://en.wikipedia.org/wiki/Standard_deviation, (see the chart in the middle of the page) we get the following probabilities:
4 SD = 99.993 666% or in other words, 1 / 15,787
5 SD = 99.999 942 6697% or in other words, 1 / 1,744,278
6 SD = 99.999 999 8027% or in other words, 1 / 506,797,346
Now, if you like round numbers then you might want to use the following (also taken from the same chart on Wikipedia):
1 out of 100,000 = 4.417 173 SD from the mean
1 out of 1,000,000 = 4.891 638 SD from the mean
1 out of 10,000,000 = 5.326 724 SD from the mean.
I don't know if it is possible for us to come to a consensus on where Lanfear is, that is, how many standard deviations is she above the mean. But if we know her level, by extrapolation we can also assign Morgase the exact opposite SD below the mean. Then we can assign Daigian and that should allow us to fill in everybody else.
Any insights are appreciated.
Thanks
The curve is not a normal distribution reflecting absolute units of strength. A normal distribution is disproven by the fact that Daigian is very close to the mean (only 12.5% of channelers fall between her and the mean according to RJ) and yet she is barely one tenth of Lanfear's strength.
Hence, the mean cannot be equidistant between Lanfear and Morgase's strengths. Hence, what we are dealing with here is a distribution skewed towards the lower side, meaning that more channelers fall on the weak side than on the strong side.
The only alternative, is that each level does not represent a set increase in raw strength, but instead represents some type of logarithmic strength increase, meaning that the distance between each consecutive SD is not set.
If it was a normal distribution, I would put Lanfear at a strength level of 1 in 150 million women. (Assuming a population of 10 billion and a 3% channeling frequency, half of whom would be women.)
There is no one that matched Lanfear, to the best of our knowledge. I think she was unique, just like I don't think Ishamael truly matched Lews Therin's strength.