Perzentile

Perzentile, also called percentile, is a statistical measure that indicates the value below which a given percentage of observations in a dataset fall. The p-th percentile is the value below which p percent of the data lie, with p between 0 and 100. The concept applies to both samples and populations, and it is commonly used to summarize distributions, compare groups, or monitor growth and performance.

Calculation relies on ordered data. A common convention places the p-th percentile at position h = p/100 × (n + 1); if h is an integer the value is the h-th data point, and if not, linear interpolation between adjacent points is used. Other conventions use h = p/100 × n. For continuous distributions, the p-th percentile is the inverse of the cumulative distribution function.

Use cases: In education and health, percentiles describe relative standing, such as standardized test scores or growth charts. Percentile ranks express the percentage of observations at or below a value. Percentiles are related to quartiles (25th, 50th, 75th), deciles (10th, 20th, etc.), and general quantiles. They are robust to extreme values and useful for comparing distributions with different shapes.

Limitations: Different calculation rules yield slightly different results in small samples; interpretation depends on the data source and method; for discrete data, many percentiles may be identical; in skewed distributions, percentiles may not reflect dispersion as well as other statistics.