Percentile, percentile rank and interpolation

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

In a distribution, the percentage of individuals whose scores are below or equal to a certain value. ¹⁾

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.

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 .

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.

Suppose the value to be solved is shown as follows:

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:

3. Calculate the equation, and get the result of .