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目录
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.
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。1)
In a distribution, the percentage of individuals whose scores are below or equal to a certain value. 2)
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 .
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:
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 .