Let X_{1:n},X_{2:n},\ldots.,X_{n:n} be a random sample of size n from a continuous population having pdf f(x) and cdf F(x).A more explicit notation of the order statistics is X_{(1,n)},X_{(2,n)},...,X_{(n,n)}.Where, 
X_{1:n}\ = the 1^{st} order statistic
       = the smallest observation        
                     = min (X_{1:n},X_{2:n},....,X_{n:n})
            {\ X}_{n:n}\ = the n^{th} order statistic
                     = the largest observation 
                     = max (X_{1:n},X_{2:n},....,X_{n:n}) 
and
              X_{r:n}= the r^{th} order statistic
                     = the  r^{th} smallest value 
Remark 1.1.The sample observation can be arranged in ascending order of magnitude such that X_{1:n}\le X_{2:n}\le\ldots..\le X_{n:n},where the numbers i=1,2,\ldots, indicate the rank of the observation in the sample.1.1 Functions of Order Statistics
Range and Mid-Range: 
A range is the distance between the smallest observation X_{1:n} and the largest observation  X_{n:n} observations.Thus, the sample median becomes
\widetilde{X}=\frac{1}{2}\left(X_{m:n}+X_{m+1:n}\right)=\frac{1}{2}\left(X_{{\frac{n}{2}}:n}+X_{{\frac{n}{2}+1}:n}\right)\ \ \ \ \                                                                                                (1.4)Remark 1.2.Remark 1.3.