percentileverdier

Percentileverdier are the values that partition a data distribution into 100 equal parts. For a given percentile p (0 < p < 100), the percentileverdien is the value below which p percent of observations fall. The 50th percentile is the median, while the 25th and 75th percentiles are the lower and upper quartiles, respectively.

There are several conventions for calculating percentileverdier. A common approach is the nearest-rank method: after sorting the data, the percentileverdien is the value with rank r = ceil(p/100 * n), where n is the number of observations. More refined methods use interpolation between adjacent values, often based on formulas like r = p/100*(n+1). Different software packages may implement varying definitions, which can yield small discrepancies, especially for small samples.

Interpretation centers on comparison and robustness. Percentileverdier summarize the distribution without assuming any specific shape, making them useful for skewed data. They indicate how a typical observation compares to the rest. For example, the 90th percentile value is the point below which 90% of observations fall, so only 10% exceed it.

Relation to percentile rank and quantiles. A percentile value is an actual data point (or an interpolated value) at a specified percentile. A percentile rank, in contrast, describes the position of a given value within the distribution as a percentile, indicating the percentage of observations below it. Percentileverdier are a fundamental component of quantile-based summaries and descriptive statistics.

Limitations and caveats include sensitivity to sample size, the handling of ties, and potential inconsistencies across calculation methods. They should be interpreted in the context of the data collection process and distribution shape.