Your Textbook Mentions That Dividing the Sample Variance by N

Essay

Your textbook mentions that dividing the sample variance by n -1 instead of n is called a degrees of freedom correction. The meaning of the term stems from the fact that one degree of freedom is used up when the mean is estimated. Hence degrees of freedom can be viewed as the number of independent observations remaining after estimating the sample mean.
Consider an example where initially you have 20 independent observations on the height of students. After calculating the average height, your instructor claims that you can figure out the height of the 20^th student if she provides you with the height of the other 19 students and the sample mean. Hence you have lost one degree of freedom, or there are only 19 independent bits of information. Explain how you can find the height of the 20^th student.