If a sample has '\(n\)' observation \(x_1, x_2, \ldots, x_n\) with '\(m\)' constraints on these values then degree of freedom of sample statistic is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(n-m\)
The degrees of freedom are the number of observations that can vary freely.
Each independent constraint fixes one value once the others are chosen. With n observations and m constraints, only \(n - m\) values are free.
For example, when the sample mean is fixed (one constraint), the n deviations from the mean add up to 0, so only \(n - 1\) of them are free.