Percentile, Percentile Rank, Interpolation

1.百分位等级 (percentile rank) ¹⁾²⁾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。

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

2.百分位数 (percentile) ：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.

3.例子：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。

• For 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.

4.注意事项：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.

1.插值法 （Interpolation）：一种求解两个数值之间某位置数值的方法。
插值法的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。

1.Interpolation: 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.

2.插值法步骤：
假设要求的数值如图所示

2.The steps of interpolation:
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）

(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）根据数据列出数据：

(2)List out by the known data:

（3）由等式求得x=56

(3)Calculate the equation, and get the result of x=56.