kvantiliseket

A kvantilis is a statistical value that divides a sorted data set into equal probability intervals. In the context of descriptive statistics, a kvantilis allows researchers to characterize the distribution of a variable by indicating the value below which a given percentage of observations fall. The most common kvantilis are the quartiles, quintiles, deciles and percentiles, each dividing the population into four, five, ten and one hundred equal parts, respectively. In a continuous distribution, the kvantilis correspond to points on the cumulative distribution function where the probability reaches a specified level, such as the 0.25‑quantile (first quartile) or the 0.75‑quantile (third quartile).

Kvantilis are defined mathematically as solutions to the equation F(x)=p, where F is the empirical or theoretical cumulative distribution function and p is a probability level between 0 and 1. For a discrete data set, common methods to estimate a kvantilis include the nearest-rank method, linear interpolation between order statistics, or the Kaplan–Meier estimator for censored data. When the data set is large, the kvantilis tend toward the true quantiles of the underlying population.

In applied fields, kvantilis are used for detecting skewness, assessing variability, constructing box plots, creating financial risk metrics such as value‑at‑risk, and defining regulatory thresholds in quality control. Because they are non-robust to outliers in some definitions, researchers often use trimmed or Winsorized kvantilis to mitigate extreme values.

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