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File:The Normal Distribution.svg

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Summary[edit]

Description
English: The re-drawn chart comparing the various grading methods in a normal distribution. Includes: Standard deviations, cumulative percentages, percentile equivalents, Z-scores and T-scores. Inspired by Figure 4.3 on Page 74 of Ward, A. W., Murray-Ward, M. (1999). Assessment in the Classroom. Belmont, CA: Wadsworth. ISBN 0534527043
Note: The 95% range is labelled as -1.98 to +1.98 standard deviations. This is probably a typographic error, as the correct range is plus or minus 1.96 standard deviations.
Date (original upload date)
Source Transferred from en.wikipedia to Commons by Abdull.
Author Heds 1 at English Wikipedia

Discussion[edit]

What is the z-score which has the steepest points of the curve? My guess it is z = -1, +1. The way to tell is to differentiate the pdf and find its maxima, but not sure if I'm up to that...

Is the 1.98 sigma/z-score for 95th percentile a typo? 1.96 is nearer 95% than 1.98 which corresponds to 95.2269%...

Y axis stands not for probability, as stated, but rather for probability density. Probability itself is zero for each given point. I think this is the important point. yes this plot is wrong !

Also, another comment: the Probability (Probability Density) cannot be negative (-1.980 or -2.580) even though the X is negative.

If you want the probability within some interval, you would calculate the integral from one endpoint to the other. With the Normal Distribution, there is no elementary anti-derivative, so the values are calculated using numerical methods. This is why you usually refer to a table that contains the calculated values. In order to use the tables you must first calculate the z-score.

Licensing[edit]

Public domain This work has been released into the public domain by its author, Heds 1 at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
Heds 1 grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Original upload log[edit]

Transferred from en.wikipedia to Commons by Abdull. The original description page was here. All following user names refer to en.wikipedia.

  • 2007-07-12 14:47 Heds 1 800×600×0 (123727 bytes) A re-drawn chart comparing the various grading methods in a normal distribution. Includes: Standard deviations, cumulative percentages, percentile equivalents, Z-scores and T-scores. Inspired by Figure 4.3 on Page 74 of Ward, A. W., Murray-Ward, M. (1999)
  • 2007-07-12 14:44 Heds 1 800×600×0 (137472 bytes) The re-drawn chart comparing the various grading methods in a normal distribution. Includes: Standard deviations, cumulative percentages, percentile equivalents, Z-scores and T-scores. Inspired by Figure 4.3 on Page 74 of Ward, A. W., Murray-Ward, M. (199

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Date/TimeThumbnailDimensionsUserComment
current05:50, 9 July 2015Thumbnail for version as of 05:50, 9 July 2015800 × 600 (121 KB)PkwywedsReverted to version as of 10:48, 23 September 2007
01:39, 3 April 2013Thumbnail for version as of 01:39, 3 April 2013725 × 437 (135 KB)青子守歌crop
10:48, 23 September 2007Thumbnail for version as of 10:48, 23 September 2007800 × 600 (121 KB)Abdull{{Information |Description=The re-drawn chart comparing the various grading methods in a normal distribution. Includes: Standard deviations, cumulative percentages, percentile equivalents, Z-scores and T-scores. Inspired by Figure 4.3 on Page 74 of Ward,

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