The upper and lower hinges are descriptive statistics of a set of 
data values, where 
is of the form 
with 
,
1, 2, .... The hinges are obtained by ordering the data in increasing order 
, ..., 
, and writing them out in the shape of a "w" as
illustrated above. The values at the bottom legs are called the hinges 
and 
(and the central peak is the statistical median).
In this ordering,
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
For 
of the form 
, the hinges 
and 
are identical to the quartiles 
and 
.
The difference 
is called the H-spread.
