Degrees of Freedom

number of unrestricted values that can be applied in any order to a distribution (Statistics)

Degrees of freedom can mean:Degrees of freedom (physics and chemistry)Degrees of freedom (engineering)Degrees of freedom (statistics)Degrees of freedom (numerics)
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Noun
1. (statistics) an unrestricted variable in a frequency distribution
(hypernym) variable, variable quantity
(classification) statistics
2. one of the minimum number of parameters needed to describe the state of a physical system
(hypernym) parameter, parametric quantity

<robotics> The number of independent parameters required to specify the position and orientation of an object. Often used to classify robot arms. For example, an arm with six degrees of freedom could reach any position close enough and could orient it's end effector (grip or tool etc.) at any angle about the three perpendicular axes.

Used in slightly different senses throughout the study of statistics, Degrees of Freedom were first introduced by Fisher based on the idea of degrees of freedom in a dynamical system (e.g., the number of independent co-ordinate values which are necessary to determine it). The degrees of freedom of a set of observations are the number of values which could be assigned arbitrarily within the specification of the system. For example, in a sample of size n grouped into k intervals, there are k-1 degrees of freedom, because k-1 frequencies are specified while the other one is specified by the total size n. Thus in a p by q contingency table with fixed marginal totals, there are (p-1)(q-1) degrees of freedom. In some circumstances the term degrees of freedom is used to denote the number of independent comparisons which can be made between the members of a sample.