Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 3 - Section 3.2 - Assess Your Understanding - Explaining the Concepts - Page 156: 49

Answer

The degrees of freedom for the sample standard deviation indicate the number of independent observations in the sample standard deviation that can take any value.

Work Step by Step

The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called the number of degrees of freedom. In other words, the number of degrees of freedom can be defined as the minimum number of independent coordinates that can specify the position of the system completely. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself, e.g., the sample variance has Nāˆ’1 degrees of freedom, since it is computed from N random scores minus the only one parameter estimated as intermediate step, which is the sample mean.
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