Statistical inference about the median from vague data

In traditional statistics all parameters of the mathematical model and possible observations should be well defined. Sometimes such assumption appears too rigid for the real-life problems, especially when dealing with imprecise or linguistic data. To relax this rigidity fuzzy methods are incorporated into statistics. The paper is devoted to statistical inference about the population median in the presence of vague data. The notion of fuzzy median is proposed. Then, a fuzzy estimator and fuzzy confidence interval for the median are suggested. Next, the problem of hypotheses testing concerning the median in the presence of imprecise data is discussed. All methods presented are distribution-free.