Who established the word " Degree of freedom " in statistics? I wonder who is the first one that established and applied the word : "degree of freedom" in 
statistics?
Why he/she need degree of freedom in the calculation of many statistical values?
 A: As with many statistical terms, it originates from the British biostatistical school in the 1920s.  To my knowledge, the concept of "degrees of freedom" within formal statistical theory was first named by Ronald Fisher.  You can find the first reference to this concept in Fisher (1922a) and it is also in his more general theoretical paper Fisher (1922b).  Prior to this there were some generic references in mathematical and philosophical discussion to "degrees of freedom" in a looser sense, but Fisher was (to my knowledge) the first to use this name to refer to specific quantities in statistical theory.
Update: Please note the comment below by T. Kasper pointing to an earlier genesis of this term in the dynamic geometry literature.

Fisher (1922a) On the interpretation of $\chi^2$ from contingency tables and the calculation of p. Journal of the Royal Statistical Society 85, pp. 87-94.
Fisher, R.A. (1922b) On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London (Series A) 222, pp. 309-368 
A: Degrees of Freedom had been used in a non-statistical sense in 1867 by Sir William Thompson and Peter G. Tait ("Treatise on Natural Philosophy") to refer to "the degrees of freedom or constraint under which the displacement takes place...;" i.e., the number of ways in which a dynamic system is free to move without violating any constraint imposed on it. R.A. Fisher was somewhat expert in complex n-coordinate geometry, so it's no surprise that he was familiar with the idea of degrees of freedom, and therefore prone to associate it with statistical variables, as noted by Ben on Apr. 19th. – T. Kasper 
