I keep seeing conflicting definitions of a statistic. Is a statistic a random variable such that it is a function of the random variables of a random sample? Or is it the value of the function of the random sample, after each random variable of the random sample has taken on a specific value?
$$(1) \ S=f(X_1,X_2...X_n)$$
$$(2) \ s=f(x_1,x_2...x_n)$$
I haven't been able to get any clarification for this and I've seen the term statistic describe both situations