What is the degree of freedom of X1Xn What is the degree of

What is the degree of freedom of (X1,.....,Xn)

What is the degree of freedom of (X1,...., Xn, Xbar)

What is the degree of freedom of of the residuals (X1-Xbar,...., Xn-Xbar)

What is the degree of freedom of (X1-Xbar,...., Xn-Xbar, Xbar)

Brief explanation please

Solution

For every value in an experiment, there will be a range. Human height can range widely so height values have a high degree of freedom and still be human height. make sense.

or each value of a parameter that you really do not know and have to estimate you lose one degree of freedom.

say for example with a t distribution, you do not know the true mean mu, you use xbar, and you do not know the true variance sigma so you use the sample standard deviation, you then lose two degrees of freedom, so in a sample of size n you have only n-2 degrees of freedom.

For x bar the values x1, x2,, ...,Xn of data, if you know xbar and the values x1, ...Xn-1, then the value of Xn is fixed, you have no freedom to have any other value.