Protractor on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way. Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and to the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved. Reading the Vernier scale: The bevel protractor Vernier scale may have graduations of 5′ (minutes) or 1/12°. Each space on the Vernier scale is 5′ less
Degrees of freedom (statistics) other distributions that arise in associated statistical testing problems. While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Although the basic concept of degrees of freedom was recognized as early as 1821 in the work of astronomer and mathematician Carl Friedrich Gauss, its modern definition and usage was first elaborated by English statistician William Sealy Gosset in his 1908 "Biometrika" article "The Probable Error of a Mean", published under the pen name "Student". While