Indicators of Relative Position

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Indicators of Relative Position
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The Normal Distribution
AKA The Bell Curve
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Percentiles, Percentile Rank

• Percentiles divide a score distribution into 100
  portions, which requires 99 percentile dividers,
  like the four dividers between the 5 fingers of a
  hand.
• A percentile is a score value at or below which a
  proportion of a score distribution falls.
• In the IQ score distribution, the score at the
  75th percentile is 110

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• An IQ score of 110 equals or exceeds 75 of the
  scores in the distribution.
• The percentile rank of a score, symbolized as
  PR(X), is the scores relative standing expressed
  as a percent.
• A person who gets 90 of the items correct on an
  exam with a score of 45 out of 50, may be at the
  75th percentile rank.
• This means that the score of 45 equaled or
  surpassed 75 of all other persons who took the
  test

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Determining Rank when all scores are given
n of scores below X n of scores in the
distribution less than X (cf value for scores
below X) n of scores at X n of scores
equal to X (cf value at score X) n total
number of scores
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X 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
f 1 3 2 5 8 7 5 2
cf 33 32 29 27 22 14 7 2
Percentile rank calculation for a score of 9
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Try it yourself
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Lets take a look at the meaning of the .5 value
in the equation. It has to do with upper lower
limits of intervals.
Interval width comes into play also. In
ungrouped distributions, interval width is 1.
9.5 9.0 8.5
Three scores of 9 spread evenly thru the interval
8.5 to 9.5
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Finding scores that correspond to a given
percentile rank can be accomplished with the
formula...
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PR 98 92 85 74 55 32 14 3
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PR 98 92 85 74 55 32 14 3
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Try it with grouped interval data. First find
the percentile rank of score14. Then find the
score that resides at the 30th percentile.
Try it again for practice First find the
percentile rank of score4. Then find the score
that resides at the 90th percentile.
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Quartiles
X 15 14 13 12 11 10
f 1 2 3 3 2 1
9
6
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The percentile scale quartile divisions should
not be confused with the standard normal
distribution
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In an ungrouped data array, you can locate the
scores that reside at the quartile divisions
X 10 9 8 7 6 5 4 3 2 1
7.5
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2.5