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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 2301 Views
Well... - 15/11/2012 07:02:45 PM 1307 Views
Hmm... - 15/11/2012 07:25:34 PM 1433 Views
see we CAN agree on stuff - 15/11/2012 07:56:12 PM 1273 Views
- 18/11/2012 08:37:22 PM 1140 Views
We've always been close with everything except the scale - 18/11/2012 10:29:07 PM 1181 Views
Re: - 18/11/2012 11:07:17 PM 1362 Views
Re: - 19/11/2012 05:16:00 AM 1192 Views
Re: - 19/11/2012 03:13:01 PM 1177 Views
They only reject 37.5%, not 62.5% - 19/11/2012 03:19:19 PM 1202 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 04:01:43 PM 1399 Views
Re: They only reject 37.5%, not 62.5% - 19/11/2012 09:04:04 PM 1157 Views
Hmmm... - 20/11/2012 02:08:40 AM 1235 Views
Perhaps, but Egwene is also being a bit dramatic in the scene as she managed - 20/11/2012 04:28:57 AM 1175 Views
Nope... - 20/11/2012 03:13:13 PM 1237 Views
I believe she is being over dramatic - 20/11/2012 03:26:24 PM 1122 Views
Keep believing that... - 20/11/2012 03:30:14 PM 1269 Views
*shrugs* - 20/11/2012 03:49:10 PM 1227 Views
Tired and forkroot are the same now? - 20/11/2012 03:55:22 PM 1104 Views
No it's the literary device - 20/11/2012 04:04:28 PM 1247 Views
This is getting ridiculous... - 20/11/2012 04:43:13 PM 1116 Views
You are missing my point completely - 20/11/2012 04:50:46 PM 1079 Views
Impossible. Daigian is exactly 0.32SD below the mean - 19/11/2012 11:06:04 AM 1182 Views
You keep saying that, but it is either a linear or a non-linear distribution - 19/11/2012 09:09:32 PM 1232 Views
That's the whole point. Thanks for finally seeing it. - 19/11/2012 09:43:27 PM 1195 Views
keep believing that ... but you making up numbers isn't really relevant *NM* - 20/11/2012 04:29:44 AM 772 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 1146 Views
Go read Fionwe's post about it *NM* - 20/11/2012 02:33:19 PM 774 Views
Is that before or after she started juicing? - 15/11/2012 11:04:14 PM 1174 Views
Wouldn't it be 1 in 105 million? - 21/11/2012 04:56:19 PM 1036 Views
Are you sure that it is a normal distribution? - 16/11/2012 04:21:02 PM 1242 Views
Ugh. I hate power level discussions. For real world applications, it should be kind of meaningless - 16/11/2012 10:28:49 PM 1133 Views
I don't really agree - 18/11/2012 08:40:53 PM 1103 Views
Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 19/11/2012 09:13:48 PM 1150 Views
Re: Perhaps, but we've seen that a MUCH weaker Channeler can win in a duel - 20/11/2012 08:10:01 AM 1124 Views
probably ... Lanfear/Cyndane is clearly remarkably skilled - 20/11/2012 02:35:09 PM 1168 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 1182 Views
You have proven nothing, except that you have an opinion *NM* - 18/11/2012 02:21:35 AM 749 Views
You simply don't get it. It is mathematically a fact. There is no opinion involved. - 18/11/2012 02:19:40 PM 1019 Views
Only because you've assigned numeric values. That you created. - 18/11/2012 02:40:51 PM 1148 Views
It doesn't matter what figure you use... - 18/11/2012 03:01:56 PM 1034 Views
What if Daigian is one third Lanfear's strength? - 18/11/2012 04:37:58 PM 1188 Views
We have a limit for Daigian's strength, as you well know. - 18/11/2012 05:41:49 PM 1155 Views
Are you kidding me? - 18/11/2012 09:07:38 PM 1279 Views
Sure you can - 18/11/2012 10:09:31 PM 1181 Views
Re: Sure you can - 18/11/2012 10:54:50 PM 1163 Views
You're right, though its 37.5% - 19/11/2012 12:21:29 AM 1116 Views
Oops, typo! - 19/11/2012 02:54:25 AM 1161 Views
Again, not possible, due to Daigian being just 0.3SD below the Mean - 19/11/2012 08:37:01 AM 1113 Views
Egwene is definitely not 2x Amys... - 19/11/2012 04:05:12 PM 1042 Views
Re: Egwene is definitely not 2x Amys... - 19/11/2012 05:55:02 PM 994 Views
Egwene is about as strong as Melaine and Amys combined - 19/11/2012 09:19:50 PM 1117 Views
Re: Egwene is about as strong as Melaine and Amys combined - 20/11/2012 02:11:26 AM 1193 Views
Forkroot in every case - 20/11/2012 04:32:26 AM 1115 Views
No! - 20/11/2012 03:15:16 PM 1105 Views
I'm not going to go re-read the books to you on this - 20/11/2012 03:39:46 PM 1131 Views
You need to read it for yourself, since you're completely confused. - 20/11/2012 03:54:26 PM 1093 Views
Not going to argue this with you. - 20/11/2012 04:09:44 PM 1050 Views
Your own example disproved your point... - 20/11/2012 04:39:25 PM 1169 Views
let's see, she's both asleep and would need hours to regain her strength - 20/11/2012 04:43:17 PM 1071 Views
Enough! - 20/11/2012 05:04:06 PM 1128 Views
LOL ... whatever. You go on believing that ... no one else sees it this way. *NM* - 20/11/2012 05:20:52 PM 737 Views
What a brilliant argument! - 20/11/2012 05:25:18 PM 1140 Views
this is why I refuse to continue this debate - 20/11/2012 05:31:11 PM 1080 Views
Re: Your own example disproved your point... - 20/11/2012 05:10:15 PM 1171 Views
Barasine + Katerine isn't that much less than - 20/11/2012 05:26:31 PM 1176 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:31:50 PM 1135 Views
Re: Barasine + Katerine isn't that much less than - 20/11/2012 05:42:53 PM 1125 Views
Excuse me? - 20/11/2012 05:28:48 PM 1179 Views
see we can agree on the relative strength of Egwene v. Forsaken - 20/11/2012 05:35:07 PM 1135 Views
??? - 20/11/2012 05:37:01 PM 1234 Views
2 middling sisters - 20/11/2012 05:45:27 PM 1166 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:26:47 AM 1071 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 09:03:40 AM 1100 Views
Re: Egwene is definitely not 2x Amys... - 20/11/2012 02:59:08 PM 1140 Views
None of this is backed by any evidence... - 20/11/2012 03:24:12 PM 1073 Views
who said Cadsuane was 1.5x Moiraine or more? - 20/11/2012 04:03:13 PM 1080 Views
Nope... - 20/11/2012 04:41:35 PM 1106 Views
wrong - 20/11/2012 04:48:50 PM 1025 Views
My bad. Mized up 1/3 and 2/3. - 20/11/2012 05:05:05 PM 1146 Views
gotcha *NM* - 20/11/2012 05:46:21 PM 705 Views
Better evidence? LOL! - 20/11/2012 03:18:55 PM 1116 Views
Huh? How did you come to that conclusion? - 20/11/2012 04:40:56 PM 1120 Views
Exactly *NM* - 20/11/2012 04:55:28 PM 1074 Views
BEcause Cadsuane is close on the heels of Egwene? - 20/11/2012 05:10:50 PM 1034 Views
I'm not arguing that. I agree that Cadsuane is pretty close to Egwene - 20/11/2012 05:50:34 PM 1154 Views
Re: Better evidence? LOL! - 20/11/2012 05:00:47 PM 1035 Views
Interesting, but let's go with your figures... - 19/11/2012 06:54:54 AM 1145 Views
Indeed - 19/11/2012 08:16:44 AM 1209 Views
Rand is sort of a special case - 20/11/2012 04:25:02 AM 1072 Views
Regarding Mesaana... - 20/11/2012 08:42:56 AM 1107 Views
You continue to mix two things - 20/11/2012 03:24:44 PM 1031 Views
No - 20/11/2012 04:54:19 PM 1265 Views
You are mistaken - 20/11/2012 05:04:40 PM 1119 Views
Yes she did Darius! - 20/11/2012 05:27:36 PM 1042 Views
Yet there is no duel - 20/11/2012 06:01:17 PM 1054 Views
Explain the .3xSD thing to me... - 19/11/2012 04:58:57 PM 1277 Views
Probably, but the AS have no idea what 37.5% means - 19/11/2012 02:59:26 AM 1071 Views
It's irrelevant - 19/11/2012 03:46:42 AM 1142 Views
Agreed. Daigian is the marker of the absolute bottom of Aes Sedai strength. - 19/11/2012 06:55:41 AM 1108 Views
Daigian - 19/11/2012 08:12:19 AM 1112 Views
It is a direct marker due to RJ's quote - 19/11/2012 08:50:26 AM 1139 Views
You missed my point - 19/11/2012 09:08:42 AM 1057 Views
Re: You missed my point - 19/11/2012 02:18:33 PM 1165 Views
Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 04:41:11 AM 1076 Views
Re: Asmodean would never have made the comment about 13 weakest AS - 20/11/2012 09:07:49 AM 1065 Views
Which would make an average AS around a 30 - 20/11/2012 04:58:56 PM 956 Views
Re: Sure you can - 19/11/2012 09:22:09 AM 1199 Views
Care to explain this... - 19/11/2012 05:06:28 PM 1022 Views
Indeed - 20/11/2012 07:16:37 AM 1224 Views
Explained far better than I ever could. Bravo. - 20/11/2012 07:30:29 AM 1078 Views
Well duh. - 20/11/2012 02:57:24 PM 1200 Views
Incorrect. - 20/11/2012 04:28:07 PM 1174 Views
No - 20/11/2012 04:44:16 PM 1164 Views
Re: No - 20/11/2012 04:48:36 PM 1134 Views
That depends... - 20/11/2012 05:18:46 PM 1005 Views
Re: That depends... - 20/11/2012 05:31:03 PM 1557 Views
You're integrating without lower limits... - 20/11/2012 02:55:06 PM 1131 Views
Re: You're integrating without lower limits... - 20/11/2012 04:37:57 PM 1177 Views
It matters. - 20/11/2012 05:22:40 PM 1153 Views
We are not talking about a normal distribution in any case - 20/11/2012 04:44:24 AM 971 Views
Re: We are not talking about a normal distribution in any case - 20/11/2012 07:02:47 AM 1178 Views
You must tell me of this special math... - 20/11/2012 03:10:09 PM 1045 Views
Re: You must tell me of this special math... - 20/11/2012 04:29:40 PM 1104 Views
Morghase is a placeholder... - 20/11/2012 04:45:42 PM 1185 Views
Re: Morghase is a placeholder... - 20/11/2012 04:49:54 PM 1477 Views
Why? - 20/11/2012 05:23:29 PM 1142 Views
Re: Why? - 20/11/2012 05:36:45 PM 1455 Views
Well... - 18/11/2012 08:43:59 PM 1177 Views
Re: Well... - 19/11/2012 03:40:44 PM 1158 Views
Wow. - 19/11/2012 03:53:47 PM 1182 Views
Re: Wow. - 19/11/2012 04:26:09 PM 1207 Views
Some points - 19/11/2012 06:03:00 PM 1250 Views
Well then you're both wrong I'm afraid - 19/11/2012 06:09:36 PM 1094 Views
Re: Well then you're both wrong I'm afraid - 19/11/2012 07:42:58 PM 961 Views
this is why I think all of the Forsaken are very close in Power - 20/11/2012 04:51:20 AM 1189 Views
Agreed - 20/11/2012 08:13:37 AM 1223 Views
probably - 20/11/2012 06:18:45 PM 1083 Views
Re: this is why I think all of the Forsaken are very close in Power - 20/11/2012 02:45:18 PM 1089 Views
I think RJ went out of his way to keep strength a bit of a mystery - 20/11/2012 08:42:44 PM 1107 Views
Indeed... - 21/11/2012 05:44:18 PM 1077 Views
I agree - 22/11/2012 01:43:02 AM 1325 Views
Math gurus...Is it possible to find the missing variable... - 21/11/2012 05:12:24 PM 1129 Views
the problem is that the Mean is not going to tell us much really - 22/11/2012 02:55:03 AM 1172 Views
Re: the problem is that the Mean is not going to tell us much really - 22/11/2012 03:15:33 AM 1499 Views
I do not think you can calculate the Mean without knowing the Units of Power - 22/11/2012 03:53:59 AM 1251 Views
Re: Math gurus...Is it possible to find the missing variable... - 23/11/2012 02:59:12 PM 1532 Views
Disregard this post *NM* - 23/11/2012 03:02:24 PM 964 Views

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