cnanydelta

valsi

cnanydelta

type

lujvo

creator

krtisfranks

time entered

Tue Apr 24 20:28:25 2018  

English

Definition #70634 - Preferred

 

definition

x₁ (li) is the (signed) difference between the average of all elements/data of x₂ (completely specified ordered multiset/list) and single number x₃ (li; default: infimum of x₂ under ordering x₆ if such is finite), using averaging function x₄ (default: arithmetic average), weights x₅ (completely specified ordered multiset/list with the same cardinality/length as x₂; default: according to notes), and inherited ordering x₆ (default: standard ordering on the set of reals).

notes

Default for x₅ is the same as the default for the weights of the given averaging function x₄, which for the arithmetic mean of a finite set is the ordered set of | x₂| terms with each term equal identically to 1/| x₂|, where "| |" represents the cardinality of its input (circumfixed). x₆ is defined on a superset of x₂ united with the singleton of x₃. The default for x₆ is mrenspoi. For example: If MATH

$x_2 = (1, 7)$

x₂ = (1, 7) and all of the defaults hold, then MATH

$x_1 = avg(1,7) - min(1,7) = 4 - 1 = 3$

x₁ = avg(1, 7) - min(1, 7) = 4 - 1 = 3; when all defaults hold and x₂ is a bounded set, x₁ is the difference between the arithmetic average of (or average of the uniform distribution on) x₂ and the infimum of x₂. See also: "sigma".

gloss words

• difference from average

created by

krtisfranks

vote information

1

time

Wed Apr 25 04:57:53 2018

Examples

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