16thlargest

16thlargest is a term used in statistics and computer science to denote the 16th largest value in a finite data set when the elements are ordered from largest to smallest. In this sense, it is a specific order statistic corresponding to k = 16. In data sets with duplicates, the 16th largest refers to the element occupying the 16th position in a non-increasing sort, counting duplicates as separate items.

Common ways to obtain the 16th largest include full sorting, selection algorithms, and heap-based approaches. A straightforward method is to sort the entire data set in descending order and select the element at index 15. More efficient in large data sets are selection algorithms such as quickselect, which finds the k-th largest in expected linear time. A min-heap of size 16 can be used; maintain the largest 16 elements seen so far, replacing the smallest in the heap when a larger value arrives; this yields O(n log 16) time and O(16) space.

Because the 16th largest depends on the ordering convention and treated duplicates, interpretations can vary; some definitions refer to the 16th largest distinct value. In streaming or time-windowed data, specialized algorithms maintain the 16th largest within a sliding window, useful for thresholding and anomaly detection. Applications include statistical summaries, percentile estimation, and financial risk measures.

As a general concept, the 16th largest is one of many order statistics used to describe the distribution of data and to support data-driven decision making. Related topics include order statistics, k-th largest algorithms, and percentile calculations.