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

===== 百分位数、百分位等级 (Percentile and percentile rank) =====

==== 百分位等级 (Percentile rank) ====

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。((《心理学名词》（第二版）：百分位数，指在整个分布中，某一值之下或等于该值的分数的百分比所对应的分数。百分等级，指在频率分布或分数群中低于给定值的那个分数的百分位数。与给定值对应。))\\
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.))

====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.

==== 例子 (Example) ====

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.

==== 注意事项 (Notes) ====

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 .

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===== 插值法 (Interpolation) =====

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.

==== 插值法步骤 (The steps of interpolation) ====

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

{{ :第二章:2.5:插值法1.svg |}}

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:

{{ :第二章:2.5:插值法2.svg |}}

3. 由等式求得结果 {{:第二章:2.5:x56.svg}}。\\
Calculate the equation, and get the result of {{:第二章:2.5:x56.svg}}.