medianes

Median, medians in mathematics, refers to two related concepts that describe a center value or line. In statistics, the median of a data set is the value that divides the ordered data into two equal halves. In plane geometry, a triangle’s median is a line segment from a vertex to the midpoint of the opposite side.

To compute the median, data are first ordered. If the number of observations n is odd, the median is the middle value; if n is even, it is the average of the two central values. The median is a measure of central tendency that is robust to outliers, in contrast to the mean. It coincides with the 50th percentile of the data distribution.

Triangle medians have properties useful in geometry and applications. There are three medians in any triangle, and they intersect at a single point called the centroid, which serves as the triangle’s center of gravity for uniform density. The centroid divides each median in a 2:1 ratio, counting from the vertex toward the midpoint. The medians partition the triangle into six smaller triangles of equal area.

In practice, medians are used in data analysis to summarize central tendency when distributions are skewed, and in geometry to compute centroids and study triangle shapes and balances.