Editing 2118: Normal Distribution
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Created by PEOPLE NEW ENOUGH TO STATISTICS TO NOT LEAVE IN ANNOYANCE. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}} | |
− | + | [[File:Empirical_Rule.PNG|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.]] | |
− | [[File: | + | 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 an infinite number of people, put them into age bins that are infinitely narrow, 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. |
− | 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 | ||
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. | 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 | + | The area between two vertical lines of the distribution represents the probability that the value is between the x-values of the lines, and the total area is 1. Randall finds the area between two ''horizontal'' lines instead, which is mathematically completely meaningless, because the y-axis of a probability distribution represents {{w|absolute magnitude|magnitude}} as a fraction of unity (although we do have half of the normal curve between the two lines). The items represented by the magnitude at any given horizontal position are indistinguishable, unordered, and interchangeable; the idea that one could be above another is meaningless, and the fact that two items happen to fall at the same position on the y-axis doesn't mean they have anything in common. So, the comic explores the humor of annoying people by deliberately misunderstanding their work. |
− | + | The title text refers to the {{w|Normal (geometry)|normal line}}, which is perpendicular to the {{w|tangent}} line at a given point. Given a shape of interest, a normal line points perpendicularly away from it at a point, making a 90-degree angle with it in all directions, while a tangent line crosses a point on it and is exactly parallel to it at that point. The normal line is not at all related to the normal distribution, as the former is a geometry concept and the latter is probability/statistics one. Saying this to a statistician would only annoy the statistician further. This refers to the fact that the diagram attempts to divide the graph with horizontal lines when such a division would usually be done with perpendicular vertical lines. | |
− | + | ==Transcript== | |
+ | {{incomplete transcript|Do NOT delete this tag too soon.}} | ||
− | + | :[A bell curve of a normal distribution, with the area between two horizontal lines shaded.] | |
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:[The center of the chart is marked between the two lines:] | :[The center of the chart is marked between the two lines:] | ||
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:[A label on the outside of the graph, describing the distance between the two lines:] | :[A label on the outside of the graph, describing the distance between the two lines:] | ||
:"Remember, 50% of the distribution falls between these two lines!" | :"Remember, 50% of the distribution falls between these two lines!" | ||
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:[Caption below the panel:] | :[Caption below the panel:] | ||
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[[Category:Charts]] | [[Category:Charts]] | ||
[[Category:Statistics]] | [[Category:Statistics]] | ||
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