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
How many standard deviations is Lanfear
- 15/11/2012 06:04:39 PM
2547 Views
Hmm...
- 15/11/2012 07:25:34 PM
1640 Views
see we CAN agree on stuff
- 15/11/2012 07:56:12 PM
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- 18/11/2012 08:37:22 PM
1345 Views
- 15/11/2012 07:56:12 PM
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- 18/11/2012 08:37:22 PM
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Re:
- 18/11/2012 11:07:17 PM
1565 Views
- 18/11/2012 11:07:17 PM
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Re:
- 19/11/2012 05:16:00 AM
1404 Views
- 19/11/2012 05:16:00 AM
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Re:
- 19/11/2012 03:13:01 PM
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- 19/11/2012 03:13:01 PM
1390 Views
They only reject 37.5%, not 62.5%
- 19/11/2012 03:19:19 PM
1437 Views
Re: They only reject 37.5%, not 62.5%
- 19/11/2012 04:01:43 PM
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Re: They only reject 37.5%, not 62.5%
- 19/11/2012 09:04:04 PM
1370 Views
Hmmm...
- 20/11/2012 02:08:40 AM
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Perhaps, but Egwene is also being a bit dramatic in the scene as she managed
- 20/11/2012 04:28:57 AM
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Nope...
- 20/11/2012 03:13:13 PM
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I believe she is being over dramatic
- 20/11/2012 03:26:24 PM
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Keep believing that...
- 20/11/2012 03:30:14 PM
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*shrugs*
- 20/11/2012 03:49:10 PM
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Tired and forkroot are the same now?
- 20/11/2012 03:55:22 PM
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No it's the literary device
- 20/11/2012 04:04:28 PM
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Impossible. Daigian is exactly 0.32SD below the mean
- 19/11/2012 11:06:04 AM
1397 Views
You keep saying that, but it is either a linear or a non-linear distribution
- 19/11/2012 09:09:32 PM
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That's the whole point. Thanks for finally seeing it.
- 19/11/2012 09:43:27 PM
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keep believing that ... but you making up numbers isn't really relevant *NM*
- 20/11/2012 04:29:44 AM
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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
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Ugh. I hate power level discussions. For real world applications, it should be kind of meaningless
- 16/11/2012 10:28:49 PM
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I don't really agree
- 18/11/2012 08:40:53 PM
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Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel
- 19/11/2012 09:13:48 PM
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Re: Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel
- 20/11/2012 08:10:01 AM
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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
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You have proven nothing, except that you have an opinion *NM*
- 18/11/2012 02:21:35 AM
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You simply don't get it. It is mathematically a fact. There is no opinion involved.
- 18/11/2012 02:19:40 PM
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Only because you've assigned numeric values. That you created.
- 18/11/2012 02:40:51 PM
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It doesn't matter what figure you use...
- 18/11/2012 03:01:56 PM
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What if Daigian is one third Lanfear's strength?
- 18/11/2012 04:37:58 PM
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Sure you can
- 18/11/2012 10:09:31 PM
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Re: Sure you can
- 18/11/2012 10:54:50 PM
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You're right, though its 37.5%
- 19/11/2012 12:21:29 AM
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Oops, typo!
- 19/11/2012 02:54:25 AM
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Again, not possible, due to Daigian being just 0.3SD below the Mean
- 19/11/2012 08:37:01 AM
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Egwene is definitely not 2x Amys...
- 19/11/2012 04:05:12 PM
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Re: Egwene is definitely not 2x Amys...
- 19/11/2012 05:55:02 PM
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Egwene is about as strong as Melaine and Amys combined
- 19/11/2012 09:19:50 PM
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Re: Egwene is about as strong as Melaine and Amys combined
- 20/11/2012 02:11:26 AM
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Forkroot in every case
- 20/11/2012 04:32:26 AM
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No!
- 20/11/2012 03:15:16 PM
1339 Views
I'm not going to go re-read the books to you on this
- 20/11/2012 03:39:46 PM
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You need to read it for yourself, since you're completely confused.
- 20/11/2012 03:54:26 PM
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Not going to argue this with you.
- 20/11/2012 04:09:44 PM
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Your own example disproved your point...
- 20/11/2012 04:39:25 PM
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let's see, she's both asleep and would need hours to regain her strength
- 20/11/2012 04:43:17 PM
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Enough!
- 20/11/2012 05:04:06 PM
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LOL ... whatever. You go on believing that ... no one else sees it this way. *NM*
- 20/11/2012 05:20:52 PM
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Re: Your own example disproved your point...
- 20/11/2012 05:10:15 PM
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Barasine + Katerine isn't that much less than
- 20/11/2012 05:26:31 PM
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Re: Egwene is definitely not 2x Amys...
- 20/11/2012 02:26:47 AM
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Re: Egwene is definitely not 2x Amys...
- 20/11/2012 09:03:40 AM
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Re: Egwene is definitely not 2x Amys...
- 20/11/2012 02:59:08 PM
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None of this is backed by any evidence...
- 20/11/2012 03:24:12 PM
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who said Cadsuane was 1.5x Moiraine or more?
- 20/11/2012 04:03:13 PM
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Nope...
- 20/11/2012 04:41:35 PM
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wrong
- 20/11/2012 04:48:50 PM
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Better evidence? LOL!
- 20/11/2012 03:18:55 PM
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Huh? How did you come to that conclusion?
- 20/11/2012 04:40:56 PM
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BEcause Cadsuane is close on the heels of Egwene?
- 20/11/2012 05:10:50 PM
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I'm not arguing that. I agree that Cadsuane is pretty close to Egwene
- 20/11/2012 05:50:34 PM
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Interesting, but let's go with your figures...
- 19/11/2012 06:54:54 AM
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Indeed
- 19/11/2012 08:16:44 AM
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Rand is sort of a special case
- 20/11/2012 04:25:02 AM
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Regarding Mesaana...
- 20/11/2012 08:42:56 AM
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You continue to mix two things
- 20/11/2012 03:24:44 PM
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No
- 20/11/2012 04:54:19 PM
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You are mistaken
- 20/11/2012 05:04:40 PM
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Probably, but the AS have no idea what 37.5% means
- 19/11/2012 02:59:26 AM
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It's irrelevant
- 19/11/2012 03:46:42 AM
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Agreed. Daigian is the marker of the absolute bottom of Aes Sedai strength.
- 19/11/2012 06:55:41 AM
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Daigian
- 19/11/2012 08:12:19 AM
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It is a direct marker due to RJ's quote
- 19/11/2012 08:50:26 AM
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You missed my point
- 19/11/2012 09:08:42 AM
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Asmodean would never have made the comment about 13 weakest AS
- 20/11/2012 04:41:11 AM
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Re: Asmodean would never have made the comment about 13 weakest AS
- 20/11/2012 09:07:49 AM
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Re: Sure you can
- 19/11/2012 09:22:09 AM
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Care to explain this...
- 19/11/2012 05:06:28 PM
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Indeed
- 20/11/2012 07:16:37 AM
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Explained far better than I ever could. Bravo.
- 20/11/2012 07:30:29 AM
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Well duh.
- 20/11/2012 02:57:24 PM
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Incorrect.
- 20/11/2012 04:28:07 PM
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No
- 20/11/2012 04:44:16 PM
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You're integrating without lower limits...
- 20/11/2012 02:55:06 PM
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We are not talking about a normal distribution in any case
- 20/11/2012 04:44:24 AM
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Re: We are not talking about a normal distribution in any case
- 20/11/2012 07:02:47 AM
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You must tell me of this special math...
- 20/11/2012 03:10:09 PM
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Re: You must tell me of this special math...
- 20/11/2012 04:29:40 PM
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Morghase is a placeholder...
- 20/11/2012 04:45:42 PM
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Well...
- 18/11/2012 08:43:59 PM
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Re: Well...
- 19/11/2012 03:40:44 PM
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Wow.
- 19/11/2012 03:53:47 PM
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Well then you're both wrong I'm afraid
- 19/11/2012 06:09:36 PM
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Re: Well then you're both wrong I'm afraid
- 19/11/2012 07:42:58 PM
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this is why I think all of the Forsaken are very close in Power
- 20/11/2012 04:51:20 AM
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Re: this is why I think all of the Forsaken are very close in Power
- 20/11/2012 02:45:18 PM
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I think RJ went out of his way to keep strength a bit of a mystery
- 20/11/2012 08:42:44 PM
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Math gurus...Is it possible to find the missing variable...
- 21/11/2012 05:12:24 PM
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the problem is that the Mean is not going to tell us much really
- 22/11/2012 02:55:03 AM
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Re: the problem is that the Mean is not going to tell us much really
- 22/11/2012 03:15:33 AM
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I do not think you can calculate the Mean without knowing the Units of Power
- 22/11/2012 03:53:59 AM
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