百分位数、百分位等级、插值法 (Percentile, percentile rank and interpolation)

某一分布中,分数 (score) 在某一值之下或等于该值的个体所占的百分比。¹⁾
In a distribution, the percentage of individuals whose scores are below or equal to a certain value. ²⁾

恰取这一值的分数称为这一百分位等级的百分位数。
The score that takes exactly this value is called the percentile of this percentile rank.

有 58% 的同学分数为 7 分或在 7 分下，则分数 X=7 的百分位等级为 58% ，这个分数就是第 58 个百分位数。
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.

在某一个案例中，分数有 1 - 5 分，对于分数 4 , 算得其对应的累积百分比是 95% ；但注意，分数 4 意味着一个人得分在 3.5 和 4.5 之间，第 95 百分位数是 4.5 ，而不是 4.0 。
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 .

插值法是一种求解两个数值之间某位置数值的方法，其假设是在所求解点的附近1个组距单位区间之内的分数和对应的百分比的变化是线性的。
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.

假设要求的数值如图所示：
Suppose the value to be solved is shown as follows:

1. 找到距求解点最近的两个区间（较远的区间不满足分数和对应的百分比线性变化的假设）。
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. 根据数据列出方程：
Make an equation based on the data:

3. 由等式求得结果 。
Calculate the equation, and get the result of .