975Perzentil

975Perzentil is not a standard statistical term. In percentile terminology, percentiles are labeled by a value between 0 and 100, such as the 97.5th percentile. If the written form "975Perzentil" was intended as "97.5th percentile" (often written as the 97.5th percentile or p = 0.975), it refers to the value below which 97.5% of observations fall. The nonstandard form may be a typographical or shorthand error.

In general, a percentile (the p-th percentile) summarizes the distribution of a variable by indicating the value below which p percent of observations lie. The 97.5th percentile is thus a high-level upper threshold used to identify extreme values, set safety or quality limits, or construct central intervals alongside other percentiles (for example, the 2.5th percentile for the lower bound of a central 95% interval).

Calculation approaches vary. For a sample of n ordered observations, common empirical estimators use formulas like k = ceil(p(n+1)) to select a value from the sorted data, sometimes with interpolation between neighboring observations. In theoretical contexts, the p-th percentile is the inverse of the distribution function F, i.e., the value x with F(x) = p.

In a normal distribution with mean μ and standard deviation σ, the 97.5th percentile equals μ + z0.975·σ, where z0.975 ≈ 1.96. This connects percentile values to standard normal quantiles and to confidence-interval construction.

Applications span growth charts, medical reference ranges, exam scoring, risk assessment, and quality control, where extreme percentiles help summarize and compare distributions.