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Indeed Tor Send a noteboard - 20/11/2012 07:16:37 AM

If 62.5% of channelers are stronger than Daigan, and strength in channeling is normally distributed, then Daigan is 0.32 standard deviations below the mean. Plain and simple.

Can you explain this? I'm not quite sure what math is being employed here.


The bell curve gives you the probability that a person has a given strength, so if you take the sum of all the probabilities for all the strengths weaker than a given person, then you find the total probability that someone is weaker than that person.

If you go to Wolfram Alpha and type in "-0.32 sd" and scroll down a little bit, you'll se a plot that illustrates this.

Of course, to begin with, we didn't know how far below the mean Daigan was, only that she was stronger than 37.5% of channelers. So to find out how many standard deviations below the mean she was, I look at a normal distribution with zero mean and standard deviation 1, and keep summing the probabilities, starting from minus infinity, and I keep it up until the sum has reached 0.375, at which point I have reached Daigan's strength (in numbers of standard deviations).

Techincally, what I do is say that the integral of exp(-0.5*(x^2))/sqrt(2 pi) from minus infinity to y should be equal to 0.375, and then solve the equation to find y.

You can do with Wolfram Alpha as well. Scroll down a little, and somewhere it says y=-0.318639, which means that Daigan is 0.318639 standard deviations below the mean.

Of course, for the real problem the mean isn't zero, and the standard deviation probably isn't 1, but the answer in terms of numbers of standard deviations is valid for all normal distributions.
Fram kamerater!
This message last edited by Tor on 20/11/2012 at 07:17:40 AM
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How many standard deviations is Lanfear - 15/11/2012 06:04:39 PM 1971 Views
Well... - 15/11/2012 07:02:45 PM 1032 Views
Hmm... - 15/11/2012 07:25:34 PM 1120 Views
see we CAN agree on stuff - 15/11/2012 07:56:12 PM 979 Views
- 18/11/2012 08:37:22 PM 887 Views
We've always been close with everything except the scale - 18/11/2012 10:29:07 PM 926 Views
Re: - 18/11/2012 11:07:17 PM 1076 Views
Re: - 19/11/2012 05:16:00 AM 922 Views
Re: - 19/11/2012 03:13:01 PM 930 Views
They only reject 37.5%, not 62.5% - 19/11/2012 03:19:19 PM 905 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 04:01:43 PM 1136 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 09:04:04 PM 875 Views
Hmmm... - 20/11/2012 02:08:40 AM 931 Views
Perhaps, but Egwene is also being a bit dramatic in the scene as she managed - 20/11/2012 04:28:57 AM 902 Views
Nope... - 20/11/2012 03:13:13 PM 933 Views
I believe she is being over dramatic - 20/11/2012 03:26:24 PM 844 Views
Keep believing that... - 20/11/2012 03:30:14 PM 968 Views
*shrugs* - 20/11/2012 03:49:10 PM 920 Views
Tired and forkroot are the same now? - 20/11/2012 03:55:22 PM 842 Views
No it's the literary device - 20/11/2012 04:04:28 PM 955 Views
This is getting ridiculous... - 20/11/2012 04:43:13 PM 832 Views
You are missing my point completely - 20/11/2012 04:50:46 PM 797 Views
Impossible. Daigian is exactly 0.32SD below the mean - 19/11/2012 11:06:04 AM 887 Views
You keep saying that, but it is either a linear or a non-linear distribution - 19/11/2012 09:09:32 PM 943 Views
That's the whole point. Thanks for finally seeing it. - 19/11/2012 09:43:27 PM 900 Views
keep believing that ... but you making up numbers isn't really relevant *NM* - 20/11/2012 04:29:44 AM 616 Views
Please show me a number that is made up. The 0.32SD for Daigian is a rule of statistics. - 20/11/2012 07:15:48 AM 868 Views
Go read Fionwe's post about it *NM* - 20/11/2012 02:33:19 PM 631 Views
Is that before or after she started juicing? - 15/11/2012 11:04:14 PM 878 Views
Wouldn't it be 1 in 105 million? - 21/11/2012 04:56:19 PM 732 Views
Are you sure that it is a normal distribution? - 16/11/2012 04:21:02 PM 968 Views
Ugh. I hate power level discussions. For real world applications, it should be kind of meaningless - 16/11/2012 10:28:49 PM 875 Views
I don't really agree - 18/11/2012 08:40:53 PM 821 Views
Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 19/11/2012 09:13:48 PM 883 Views
Re: Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 20/11/2012 08:10:01 AM 859 Views
probably ... Lanfear/Cyndane is clearly remarkably skilled - 20/11/2012 02:35:09 PM 880 Views
Since I've proven that it's not a normal distribution in units of absolute strength, SDs don't apply - 17/11/2012 07:48:21 PM 906 Views
You have proven nothing, except that you have an opinion *NM* - 18/11/2012 02:21:35 AM 603 Views
You simply don't get it. It is mathematically a fact. There is no opinion involved. - 18/11/2012 02:19:40 PM 748 Views
Only because you've assigned numeric values. That you created. - 18/11/2012 02:40:51 PM 866 Views
It doesn't matter what figure you use... - 18/11/2012 03:01:56 PM 762 Views
What if Daigian is one third Lanfear's strength? - 18/11/2012 04:37:58 PM 889 Views
We have a limit for Daigian's strength, as you well know. - 18/11/2012 05:41:49 PM 853 Views
Are you kidding me? - 18/11/2012 09:07:38 PM 1012 Views
Sure you can - 18/11/2012 10:09:31 PM 917 Views
Re: Sure you can - 18/11/2012 10:54:50 PM 866 Views
You're right, though its 37.5% - 19/11/2012 12:21:29 AM 834 Views
Oops, typo! - 19/11/2012 02:54:25 AM 904 Views
Again, not possible, due to Daigian being just 0.3SD below the Mean - 19/11/2012 08:37:01 AM 833 Views
Egwene is definitely not 2x Amys... - 19/11/2012 04:05:12 PM 794 Views
Re: Egwene is definitely not 2x Amys... - 19/11/2012 05:55:02 PM 727 Views
Egwene is about as strong as Melaine and Amys combined - 19/11/2012 09:19:50 PM 847 Views
Re: Egwene is about as strong as Melaine and Amys combined - 20/11/2012 02:11:26 AM 857 Views
Forkroot in every case - 20/11/2012 04:32:26 AM 843 Views
No! - 20/11/2012 03:15:16 PM 837 Views
I'm not going to go re-read the books to you on this - 20/11/2012 03:39:46 PM 841 Views
You need to read it for yourself, since you're completely confused. - 20/11/2012 03:54:26 PM 808 Views
Not going to argue this with you. - 20/11/2012 04:09:44 PM 784 Views
Your own example disproved your point... - 20/11/2012 04:39:25 PM 862 Views
let's see, she's both asleep and would need hours to regain her strength - 20/11/2012 04:43:17 PM 774 Views
Enough! - 20/11/2012 05:04:06 PM 849 Views
LOL ... whatever. You go on believing that ... no one else sees it this way. *NM* - 20/11/2012 05:20:52 PM 588 Views
What a brilliant argument! - 20/11/2012 05:25:18 PM 881 Views
this is why I refuse to continue this debate - 20/11/2012 05:31:11 PM 818 Views
Re: Your own example disproved your point... - 20/11/2012 05:10:15 PM 901 Views
Barasine + Katerine isn't that much less than - 20/11/2012 05:26:31 PM 898 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:31:50 PM 829 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:42:53 PM 834 Views
Excuse me? - 20/11/2012 05:28:48 PM 889 Views
see we can agree on the relative strength of Egwene v. Forsaken - 20/11/2012 05:35:07 PM 838 Views
??? - 20/11/2012 05:37:01 PM 929 Views
2 middling sisters - 20/11/2012 05:45:27 PM 864 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:26:47 AM 775 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 09:03:40 AM 829 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:59:08 PM 874 Views
None of this is backed by any evidence... - 20/11/2012 03:24:12 PM 776 Views
who said Cadsuane was 1.5x Moiraine or more? - 20/11/2012 04:03:13 PM 789 Views
Nope... - 20/11/2012 04:41:35 PM 830 Views
wrong - 20/11/2012 04:48:50 PM 762 Views
My bad. Mized up 1/3 and 2/3. - 20/11/2012 05:05:05 PM 850 Views
gotcha *NM* - 20/11/2012 05:46:21 PM 548 Views
Better evidence? LOL! - 20/11/2012 03:18:55 PM 846 Views
Huh? How did you come to that conclusion? - 20/11/2012 04:40:56 PM 833 Views
Exactly *NM* - 20/11/2012 04:55:28 PM 795 Views
BEcause Cadsuane is close on the heels of Egwene? - 20/11/2012 05:10:50 PM 740 Views
I'm not arguing that. I agree that Cadsuane is pretty close to Egwene - 20/11/2012 05:50:34 PM 856 Views
Re: Better evidence? LOL! - 20/11/2012 05:00:47 PM 764 Views
Interesting, but let's go with your figures... - 19/11/2012 06:54:54 AM 895 Views
Indeed - 19/11/2012 08:16:44 AM 928 Views
Rand is sort of a special case - 20/11/2012 04:25:02 AM 751 Views
Regarding Mesaana... - 20/11/2012 08:42:56 AM 835 Views
You continue to mix two things - 20/11/2012 03:24:44 PM 749 Views
No - 20/11/2012 04:54:19 PM 979 Views
You are mistaken - 20/11/2012 05:04:40 PM 825 Views
Yes she did Darius! - 20/11/2012 05:27:36 PM 771 Views
Yet there is no duel - 20/11/2012 06:01:17 PM 756 Views
Explain the .3xSD thing to me... - 19/11/2012 04:58:57 PM 1006 Views
Probably, but the AS have no idea what 37.5% means - 19/11/2012 02:59:26 AM 797 Views
It's irrelevant - 19/11/2012 03:46:42 AM 834 Views
Agreed. Daigian is the marker of the absolute bottom of Aes Sedai strength. - 19/11/2012 06:55:41 AM 811 Views
Daigian - 19/11/2012 08:12:19 AM 851 Views
It is a direct marker due to RJ's quote - 19/11/2012 08:50:26 AM 854 Views
You missed my point - 19/11/2012 09:08:42 AM 808 Views
Re: You missed my point - 19/11/2012 02:18:33 PM 855 Views
Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 04:41:11 AM 814 Views
Re: Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 09:07:49 AM 783 Views
Which would make an average AS around a 30 - 20/11/2012 04:58:56 PM 657 Views
Re: Sure you can - 19/11/2012 09:22:09 AM 929 Views
Care to explain this... - 19/11/2012 05:06:28 PM 786 Views
Indeed - 20/11/2012 07:16:37 AM 998 Views
Explained far better than I ever could. Bravo. - 20/11/2012 07:30:29 AM 804 Views
Well duh. - 20/11/2012 02:57:24 PM 918 Views
Incorrect. - 20/11/2012 04:28:07 PM 907 Views
No - 20/11/2012 04:44:16 PM 881 Views
Re: No - 20/11/2012 04:48:36 PM 865 Views
That depends... - 20/11/2012 05:18:46 PM 739 Views
Re: That depends... - 20/11/2012 05:31:03 PM 1156 Views
You're integrating without lower limits... - 20/11/2012 02:55:06 PM 856 Views
Re: You're integrating without lower limits... - 20/11/2012 04:37:57 PM 877 Views
It matters. - 20/11/2012 05:22:40 PM 860 Views
We are not talking about a normal distribution in any case - 20/11/2012 04:44:24 AM 680 Views
Re: We are not talking about a normal distribution in any case - 20/11/2012 07:02:47 AM 872 Views
You must tell me of this special math... - 20/11/2012 03:10:09 PM 778 Views
Re: You must tell me of this special math... - 20/11/2012 04:29:40 PM 811 Views
Morghase is a placeholder... - 20/11/2012 04:45:42 PM 886 Views
Re: Morghase is a placeholder... - 20/11/2012 04:49:54 PM 1071 Views
Why? - 20/11/2012 05:23:29 PM 857 Views
Re: Why? - 20/11/2012 05:36:45 PM 1028 Views
Well... - 18/11/2012 08:43:59 PM 926 Views
Re: Well... - 19/11/2012 03:40:44 PM 894 Views
Wow. - 19/11/2012 03:53:47 PM 935 Views
Re: Wow. - 19/11/2012 04:26:09 PM 954 Views
Some points - 19/11/2012 06:03:00 PM 969 Views
Well then you're both wrong I'm afraid - 19/11/2012 06:09:36 PM 788 Views
Re: Well then you're both wrong I'm afraid - 19/11/2012 07:42:58 PM 697 Views
this is why I think all of the Forsaken are very close in Power - 20/11/2012 04:51:20 AM 885 Views
Agreed - 20/11/2012 08:13:37 AM 912 Views
probably - 20/11/2012 06:18:45 PM 810 Views
Re: this is why I think all of the Forsaken are very close in Power - 20/11/2012 02:45:18 PM 827 Views
I think RJ went out of his way to keep strength a bit of a mystery - 20/11/2012 08:42:44 PM 843 Views
Indeed... - 21/11/2012 05:44:18 PM 801 Views
I agree - 22/11/2012 01:43:02 AM 1064 Views
Math gurus...Is it possible to find the missing variable... - 21/11/2012 05:12:24 PM 826 Views
the problem is that the Mean is not going to tell us much really - 22/11/2012 02:55:03 AM 907 Views
Re: Math gurus...Is it possible to find the missing variable... - 23/11/2012 02:59:12 PM 1136 Views
Disregard this post *NM* - 23/11/2012 03:02:24 PM 803 Views

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