thirdhighest

Thirdhighest is a term used to denote the third-largest value in a collection of numbers or items. In computing, statistics, and data analysis, it appears in contexts such as rankings, leaderboards, and numerical summaries.

There are two common interpretations. The third-highest value counting duplicates refers to the third element when the data are sorted in descending order, allowing repeated values to occupy multiple positions. The third-highest distinct value, by contrast, considers only distinct values after removing duplicates. For example, in the list [7, 2, 7, 4, 9, 9, 3], the third-highest (counting duplicates) is 7, while the third-highest distinct value is 4.

Computing methods vary by context and data size. A simple approach is to sort the data in descending order and select the third element. More efficient methods for large datasets include maintaining the top three values in a single pass, or using a selection algorithm (such as quickselect) to find the k-th largest value. For the third-highest distinct value, one can first deduplicate the input or maintain a min-heap of the three largest distinct values.

Edge cases include datasets with fewer than three elements, where the third-highest may be undefined; implementations may return null, NaN, or the highest available value. The concept is related to order statistics and is often used in ranking, statistics, and algorithm design to extract relative positioning within a dataset. See also: nth order statistic, top-k, ranking.