mediaan

Mediaan is the Dutch term for the median, used in both statistics and geometry, describing a central or middle element in different contexts.

In statistics, the mediaan is a measure of central tendency that identifies the middle value of an ordered data set. If there are an odd number n of observations, the mediaan is the value at position (n+1)/2. If n is even, it is the average of the two central values. The mediaan splits the data into two halves, with about 50% of observations at or below and at or above it. It is robust to outliers, making it a common choice for skewed distributions. In population terms, the mediaan is a value m such that P(X ≤ m) ≥ 0.5 and P(X ≥ m) ≥ 0.5. The mediaan corresponds to the 50th percentile and is often shown as the central line in box plots.

In geometry, a triangle’s mediaan is a line segment from a vertex to the midpoint of the opposite side. The three medians intersect at the centroid, which lies two-thirds of the way from each vertex to the opposite side along the median. The medians divide the triangle into six smaller triangles of equal area. If coordinates are used, the centroid is located at the average of the vertex coordinates: ((x1+x2+x3)/3, (y1+y2+y3)/3). The length of a median can be computed by Apollonius’s theorem: m_a^2 = (2b^2 + 2c^2 − a^2)/4, where a, b, c are the side lengths.

Beyond mathematics, the term mediaan is sometimes used in data visualization to denote the central line of a box plot.