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Rank in Statistics 📂Statistical Test

Rank in Statistics

Definition

In statistics, the rank R:R→NR : \mathbb{R} \to \mathbb{N} is commonly used as a function to indicate the order of data when sorted in ascending order.

Explanation

x3<x1<x2  ⟹  x(1)=x3,x(2)=x1,x(3)=x2 x_{3} < x_{1} < x_{2} \implies x_{(1)} = x_{3}, x_{(2)} = x_{1}, x_{(3)} = x_{2} In statistics, the method of placing parentheses in the subscript of data is used when the order of data is required. The rank introduced in the definition can be expressed as a function of a random variable as follows, even if the data is not fixed. R(X)=n,X:Ω→R R(X) = n \qquad , X : \Omega \to \mathbb{R} This means that the random variable XX is the nnth smallest in the entire sample.

See Also