ABSTRACT. Mode and median are two of the most important statistics we use when we analyze data. In this paper, we consider data structures and algorithms for preprocessing a labelled list of length n so that, for any given i and j we can answer queries of the form: What is the mode or median label in the sequence of labels between indices i and j. Our results are on an approximate version of this problem. Using O(n/(1 − α)) space, our data structure can find in O(log log 1 α n) time an element whose number of occurrences is at least α times of that of the mode, for some user-specified parameter 0 < α < 1. Data structures are proposed to achieve constant query time for α = 1/2, 1/3 and 1/4, using storage space of n log n, n log log n and n, respectively. We also show that if the elements are comparable, an O(n/(1−α)) space, O(1) query time data structure can answer range median queries with a guaranteed accuracy of α × |j − i + 1|/2 .