Estimation of the finite population distribution function and related statistics, such as the median and interquartile range, is considered. Large-sample properties of estimators constructed from stratified cluster samples, and properties of large-sample confidence intervals, are established. The results are obtained within the context of a sequence of finite populations generated from a superpopulation.
"Quantile Estimation with a Complex Survey Design." Ann. Statist. 19 (1) 454 - 469, March, 1991. https://doi.org/10.1214/aos/1176347993