medians

In geometry, medians of a triangle are the line segments joining each vertex to the midpoint of the opposite side. The three medians intersect at a single point called the centroid, which serves as the triangle’s center of mass for a lamina of uniform density. The centroid divides each median in a 2:1 ratio, with the longer portion nearer the vertex.

Analytically, the centroid of a triangle with vertices at A(x1,y1), B(x2,y2), and C(x3,y3) is at ((x1+x2+x3)/3, (y1+y2+y3)/3). If the side lengths opposite A, B, and C are a, b, and c, the length of the median from A to the midpoint of BC is m_a = (1/2) sqrt(2b^2 + 2c^2 - a^2).

In statistics, the median is a measure of central tendency defined as the middle value of an ordered data set. For an odd number of observations, it is the central value; for an even number, it is typically the average of the two central values. The median is robust to outliers and is widely used in descriptive statistics, nonparametric methods, and box plots to summarize data.