Quantile

A distribution-free (non-parametric) quantile estimator based on the order statistics (the sorted values in the sample).

There are several definitions for the quantile estimator useful in defining reference limits.

Formula (N is the sample size and p is the quantile) Description
Np+1/2 Piecewise linear function where the knots are the values midway through the steps of the empirical distribution function. Recommended by Linnet (2000) as having the lowest root-mean-squared-error .
(N+1)p Linear interpolation of the expectations for the order statistics of the uniform distribution on [0,1]. Recommended by IFCC (1987) and CLSI (2010).
(N+1/3)p+1/3 Linear interpolation of the approximate medians for the order statistics. Has many excellent properties and is approximately median-unbiased regardless of the distribution.

A 95% reference interval (0.025 and 0.975 quantiles) requires a minimum sample size of 39. A 90% confidence interval for a 95% reference interval requires a minimum sample size of 119.