Question

Choose the correct meaning of degrees of freedom in statistical concept if \(n\) is number of observations.

• A. Number of independent observations
• B. Number of dependent observations
• C. Either independent or dependent observations
• D. Neither independent nor dependent observations

Hint:

For sample variance: \[ \text{Degrees of Freedom}=n-1 \] because one observation becomes dependent after fixing the sample mean.

Answer 1

The Correct Option is A

Step 1: Understand the idea of freedom.
Suppose there are \[ n \] observations. If no restrictions are imposed, all observations can vary independently.

Step 2: Consider one constraint.
For example, if the sample mean is fixed, then after choosing \[ n-1 \] values freely, the last value is automatically determined. Therefore, \[ \text{Degrees of Freedom}=n-1 \]

Step 3: Interpret the definition.
Degrees of freedom always refer to the number of independent observations available. Thus the correct interpretation is: \[ {\text{Number of independent observations}} \]