Percentile

In statistics, a percentile or percentile score, also known as centile (often denoted as P k {\displaystyle P_{k}} or Pk, for a given percentage k), is a score greater than a given percentage of all scores (or data point value) in a sample. I.e., a score in the k-th percentile would be above approximately k% of all scores in its sample. For example, the 97th percentile (P97) is the value such that 97% of the data points are less than it. Percentiles are a type of quantiles, obtained by a subdivision into 100 groups. The 25th percentile (P25) is also known as the first quartile (Q1), the 50th percentile (P50) as the median or second quartile (Q2), and the 75th percentile (P75) as the third quartile (Q3). For example, the 50th percentile (median) is the score below (or at or below, depending on the definition) which 50% of the scores in the distribution are found. Percentiles are expressed in the same unit of measurement as the input scores, not in percent; for example, if the scores refer to human weight, the corresponding percentiles will be expressed in kilograms or pounds. In the limit of an infinite sample size, the percentile approximates the percentile function, the inverse of the cumulative distribution function. A related quantity is the percentile rank of a given score, expressed as a percentage, which represents the fraction of scores in its distribution that are less than it, an exclusive definition. Percentile scores and percentile ranks are often used in the reporting of test scores from norm-referenced tests, but, as just noted, they are not the same. For percentile ranks, a score is given and a percentage is computed. Percentile ranks are exclusive: if the percentile rank for a specified score is 90%, then 90% of the scores...