2118: Normal Distribution - Revision history

SomebodyElse: /* Explanation */ just linking characters' names

2026-05-13T12:35:09Z

‎Explanation: just linking characters' names

172.70.162.134: /* Explanation */

2023-03-02T14:01:34Z

‎Explanation

Kynde: /* Explanation */

2023-03-02T10:17:17Z

‎Explanation

172.71.154.89 at 18:23, 1 March 2023

2023-03-01T18:23:43Z

Maria D. Armstrong: 20 didn't do it; I give up

2022-06-06T17:42:19Z

20 didn't do it; I give up

Maria D. Armstrong: Undo revision 286337 by Maria D. Armstrong (talk)

2022-06-06T17:41:38Z

Undo revision 286337 by Maria D. Armstrong (talk)

Maria D. Armstrong: Undo revision 286336 by Maria D. Armstrong (talk)

2022-06-06T17:40:53Z

Undo revision 286336 by Maria D. Armstrong (talk)

Maria D. Armstrong: Undo revision 286335 by Maria D. Armstrong (talk)

2022-06-06T17:40:23Z

Undo revision 286335 by Maria D. Armstrong (talk)

Maria D. Armstrong: Undo revision 286334 by Maria D. Armstrong (talk)

2022-06-06T17:39:49Z

Undo revision 286334 by Maria D. Armstrong (talk)

Maria D. Armstrong: Undo revision 286333 by Maria D. Armstrong (talk)

2022-06-06T17:38:58Z

Undo revision 286333 by Maria D. Armstrong (talk)

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 Many statistical samplings resemble a pattern called a "{{w|normal distribution}}".  A theoretically perfect normal distribution would have an infinite sample size and infinitely small bins.  That would produce a bar chart matching the shape of the curve in the comic.
-The area between two vertical lines of the distribution represents the probability that a randomly selected X-value is between the X-values of the lines. Randall instead finds the area between two ''horizontal'' lines, which is mathematically meaningless, because the Y-axis of a probability distribution is typically taken to represent {{w|absolute magnitude|magnitude}} as a fraction of unity. In the age-distribution analogy above, two points with the same X-value could be understood to represent two people with the same age; but two points with the same Y-value cannot easily be understood in terms of the analogy. The items "represented" by the magnitude at any given horizontal position are indistinguishable, unordered, and interchangeable; the fact that two items happen to fall at the same position on the Y-axis doesn't mean they have anything in common.
+The area between two vertical lines of the distribution represents the probability that a randomly selected X-value is between the X-values of the lines. [[Randall]] instead finds the area between two ''horizontal'' lines, which is mathematically meaningless, because the Y-axis of a probability distribution is typically taken to represent {{w|absolute magnitude|magnitude}} as a fraction of unity. In the age-distribution analogy above, two points with the same X-value could be understood to represent two people with the same age; but two points with the same Y-value cannot easily be understood in terms of the analogy. The items "represented" by the magnitude at any given horizontal position are indistinguishable, unordered, and interchangeable; the fact that two items happen to fall at the same position on the Y-axis doesn't mean they have anything in common.
 In short, Randall has invented a new probability distribution, which the title text humorously implies should be called the ''tangent distribution''. This distribution is defined as follows: consider the area between the curve in the comic and the horizontal axis, and consider a random point (X, Y) uniformly distributed in that region.  Then X has the normal distribution and Y has the tangent distribution.  Areas between vertical lines in the comic give probabilities concerning X, and areas between horizontal lines in the comic give probabilities concerning Y.  The comic correctly indicates that if we let ''R'' be the interval of Y values that is 52.682% of the range of Y centered at the midpoint of the range, then any randomly selected Y value has probability 1/2 of falling inside interval ''R''.

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 ==Explanation==
-This is another comic on [[:Category:How to annoy|How to annoy]] people, here in particular a statistician.
+This is another comic on [[:Category:How to annoy|How to annoy]] people, particularly targeting statisticians in this instance.
 [[File:Standard_deviation_diagram.svg|thumb|{{w|Normal distribution}}s and the intervals of the standard deviation are a topic commonly seen in introductory statistics.  Randall's chart is similar, but his lines are perpendicular.]]

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 ==Explanation==
 [[File:Standard_deviation_diagram.svg|thumb|{{w|Normal distribution}}s and the intervals of the standard deviation are a topic commonly seen in introductory statistics.  Randall's chart is similar, but his lines are perpendicular.]]
 In statistics, a {{w|Probability distribution|distribution}} is a representation that can be understood in terms of how much of a sample is expected to fall into either discrete bins or between particular ranges of values.  For example, if you wanted to represent an age distribution using bins of ten years (0-9, 10-19, etc.), you could produce a bar chart, one bar for each bin, where the height of each bar represents a count of the portion of the sample matching that bin. To turn that bar chart into a distribution, you'd get infinitely many people (technically: a number N which tends to infinity), put them into age bins that are infinitely narrow (technically: bins whose size is O(1/sqrt(N))), and then divide each bin count by the total count so that the whole thing added up to 1. It is common to ask how much of the distribution lies between two vertical lines; that would correspond to asking what percent of people are expected to fall between two ages.

← Older revision		Revision as of 18:23, 1 March 2023
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	[[Category:Statistics]]		[[Category:Statistics]]
	[[Category:Puns]]		[[Category:Puns]]
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 {{comic
 | number    = 2118
-| date      = March 01, 2019
+| date      = March 1, 2019
 | title     = Normal Distribution
 | image     = normal_distribution.png