Kvantiiles

Kvantiiles, also known as quantiles, are statistical measures that divide a dataset into equal-sized groups or segments. They are used to describe the distribution of values within a dataset and provide insights into the spread and central tendency of the data. Quantiles are particularly useful in fields such as statistics, finance, engineering, and data science for summarizing and analyzing distributions.

The most commonly used quantiles are quartiles, which divide data into four equal parts, and percentiles, which divide data into 100 equal parts. For example, the median is a special case of a quantile, specifically the 50th percentile, representing the middle value of a dataset. Other quantiles include deciles (dividing data into ten parts) and quintiles (dividing data into five parts). The general term "quantile" refers to any value that divides the dataset into continuous proportions, such as the 25th quantile (first quartile) or the 75th quantile (third quartile).

Quantiles are calculated based on the ordered values of a dataset. The method of calculation can vary depending on the definition used, such as the method of linear interpolation or nearest-rank methods. For instance, the *n*th quantile of a dataset with *N* observations can be approximated by finding the position *p* = (*n*/*100*) × (*N* + 1) and selecting the corresponding value or interpolating between adjacent values.

Quantiles are widely used in descriptive statistics to summarize data distributions, in exploratory data analysis to identify outliers or skewness, and in inferential statistics to construct confidence intervals and hypothesis tests. They are also fundamental in robust statistical methods, where they provide resistance to extreme values that could skew traditional measures like the mean. Applications include risk assessment in finance, quality control in manufacturing, and performance evaluation in sports and education.