A correction which must be applied to the measured moments 
obtained from normally
distributed data which have been binned in order to obtain
correct estimators 
for the population moments 
. The corrected versions of the second, third, and fourth
moments are then
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the class interval.
If 
is the 
th
cumulant of an ungrouped distribution and 
the 
th cumulant of the grouped distribution
with class interval 
, the corrected cumulants (under rather restrictive conditions)
are
 |
(4)
|
where 
is the 
th
Bernoulli number, giving
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  |  |
(9)
|
 |  |  |
(10)
|
For a proof, see Kendall et al. (1998).
