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====== Percentile, percentile rank and interpolation ======

===== Percentile and percentile rank =====

==== Percentile ====

The score that takes exactly this value is called the percentile of this percentile rank.

==== Percentile rank ====

In a distribution, the percentage of individuals whose scores are **below or equal** to a certain value. ((APA Dictionary: Percentile, the location of a score in a distribution expressed as the percentage of cases in the data set with scores equal to or below the score in question. Thus, if a score is said to be in the 90th percentile this means that 90% of the scores in the distribution are equal to or lower than that score. Also called percentile rank.))

==== Example ====

If 58% of the students have a score of 7 or below, the percentile rank of X=7 is 58% , so the X=7 is the 58th percentile.

==== Notes ====

In one case, the score is 1 - 5 , and for a score of 4 , the corresponding cumulative percentage is 95% ; but note that a score of 4 means that a person scores between 3.5 and 4.5 , and the 95th percentile is 4.5 , not 4.0 .

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===== Interpolation =====

Interpolation is a method to calculate the value of a certain number between two numbers. The hypothesis of interpolation is that, the change in scores and percentages within a unit interval of 1 group distance around the solved point is linear.

==== The steps of interpolation ====

Suppose the value to be solved is shown as follows: 

{{ :第二章:2.5:插值法1.svg |}}

1. Find the 2 nearest intervals to the value to be solves (Further intervals do not requires the hypothesis of scores and percentages changing linearly). 

2. Make an equation based on the data:

{{ :第二章:2.5:插值法2.svg |}}

3. Calculate the equation, and get the result of {{:第二章:2.5:x56.svg}}.