median
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median
median
see MEASURES OF CENTRAL TENDENCY.median
[′mē·dē·ən]Median
in geometry, the line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are concurrent. Their common point is called the centroid of the triangle. The centroid of a triangle cut out of material of uniform density is the center of gravity. It is also the center of gravity of a system of three equal masses situated at the vertices of the triangle. The medians of a triangle divide one another in the ratio 2:1 reckoning from the vertex to the base.
Median
in probability theory, one of the characteristics of the distribution of values of a random variable. For a random variable X with continuous distribution function F(x), the median m is defined as the root of the equation
The random variable X assumes values larger than m with probability ½ and values smaller than m with the same probability.
In mathematical statistics, the median of an ordered sequence of n quantities x1 ≤ x2 ≤ • • • ≤ xn is either xk, if n is odd and equal to 2k + 1, or (xk + xk+1)/2, if n is even and equal to 2k. As an estimate of the median for independent observations of a random variable X, we take the median of the ordered sequence constructed from the results of the observations.