fifthlargest

The fifth largest is the element that ranks fifth when a finite set of numbers is arranged in nonincreasing order. It is the fifth order statistic, often denoted as the k-th order statistic with k = 5. In a data set where duplicates occur, the fifth position is determined by the sorted sequence, unless a convention uses distinct values only.

If the data set contains fewer than five elements, the fifth largest is undefined under standard definitions. Some practical conventions may treat the value as absent or as a special placeholder in algorithms or databases.

Computationally, the fifth largest can be obtained by sorting the entire set and selecting the fifth element from the top. More efficient approaches exist for large data sets or streaming data, such as using a quickselect algorithm to locate the fifth largest without full sorting, or maintaining a min-heap of size five to track the top five values as data arrives.

There is an important distinction between the fifth largest value and the fifth largest distinct value. The former counts duplicates toward the ranking, while the latter considers only distinct values, which can yield a different result when repeated numbers are present.

Applications of the concept include data analysis and ranking tasks, sports standings, financial or scientific data evaluations, and database queries that retrieve top-k results. The broader area is the study of order statistics and selection problems in computer science and statistics.