Vol. 4, No. 11

Congratulations! 
You're right!

Mark Miwerds is on the right track with the term 'degrees of freedom, ' but that's about it.
Degrees of freedom is a concept that is often difficult for students to understand. One way that I often explain it is by looking at the example below.
 
           

In this case, these four numbers are used to calculate the sample standard deviation (S).
 
To calculate the standard deviation, one must use the mean
 
           
             
           
Students can then be asked whether they could determine the third number if they had two numbers from a sample of three, as well as the mean of these numbers. For example, if
X₁ =  7, X₂  =  10, and the mean is 10, could one determine the value of X₃? Using intuition, it is clear that the only value that X₃ could be is 13. This number cannot vary; thus the meaning of 'limited degree of freedom. '           
 
A second intuitive approach is to remind students that a sample standard deviation (S) is an estimage of a population's standard deviation By dividing by  n ' 1 rather than by n, the sample standard deviation will be larger, giving more 'wiggle room ' when one uses S  as an estimate of. In this case, one would divide by 2 rather than 3. If the sample size were 100, would this make much difference?