g01alf

Purpose

Synopsis

[res,ifail] = g01alf(x<,ifail>)

Description

 
 G01ALF calculates the minimum, lower hinge, median, upper hinge 
 and the maximum of a sample of n observations.
 
 The data consist of a single sample of n observations denoted by 
 x  and let z , for i=1,2,...,n represent the sample observations 
  i          i                                                   
 sorted into ascending order.
 
        n                   (n+1)         
 Let m= - if n is even and  ----- if n is odd,
        2                     2           
 
        m                   (m+1)         
 and k= - if m is even and  ----- if m is odd.
        2                     2           
 
 Then we have;
 
     Minimum      =   z ,          
                       1           
 
     Maximum      =   z ,          
                       n           
 
     Median       =   z            if n is odd,
                       m           
 
                       z +z        
                        m  m+1     
                  =    -------     if n is even,
                          2        
 
     Lower hinge  =   z            if m is odd,
                       k           
 
                       z +z        
                        k  k+1     
                  =    -------     if m is even,
                          2        
 
     Upper hinge  =   z            if m is odd,
                       n-k+1       
 
                       z   +z      
                        n-k  n-k+1 
                  =    ----------- if m is even.
                            2      
 

Parameters

g01alf

Required Input Arguments:

x (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

res (5)                               real
ifail                                 integer