What is meant by the termSolutionDegrees of freedom it is n

What is meant by the term

Solution

Degrees of freedom : it is number of values in a calculation that are free to vary.

Suppose we have two sample data points x₁ and x₂.

X_avg = (x₁ + x₂) / 2

Now suppose x₁ = 4 and X_avg = 6. Value of x₂ can be determined by X_avg formula. It means value of x₂ is fixed. SO only x₁ is free to vary. So degrees of freedom = 1

Now take another example:

Suppose we have now three data point x₁ , x₂ and x₃.

Now X_avg = (x₁ + x₂ + x₃) / 2 .

suppose x₁ = 5, x₂ = 7 and X_avg = 6. no value of x₃ can be determined using X_avg formula. so value of x₃ is fixed. Only x₁ and x₂ can vary freely. SO degreed of freedom = 2

General formula: No. of degrees of freedom in a calculation is equal to total no of observations (n) minus no of estimated needed (k) in the intermediate steps.

degrees of freedom = n - k

In the above examples No of estimated needed was X_avg. k = 1

In the first example n =2 and k =1. so degrees of freedom = 2 -1 = 1

In the second example n = 3 and k = 1. so degrees of freedom = 3 -1 = 2