Calculates the frequency table with respect to the open left boundary convention for a discrete data set.
Say for example the boundary points used are {b_1, b_2, ..., b_n}
,
now the first term of the array returned which represents the frequency table, is the
number of elements from the data set within the interval (-infinity, b_1)
,
the second term of the array returned is the number of elements from the data set within
the interval [b_1, b_2)
, and so on...
Note that before this method is called you are required it to set the discrete data set and the boundaries intervals are set to calling SetDataSet and SetBoundariesIntervals respectively.
Consider the set of boundaries { 1, 2, 3, 4, 5 }
, which divide the real
line into six sub-intervals. Now if we use the open left boundary convention then the
real line will be divided into the sub-intervals:
(-infinity, 1], (1,2], (2,3], (3,4], (4,5], (5, infinity)
Note that, each point on the real line can be assigned to one of these sub-intervals
and therefore when assigning a data point to one of these intervals there will only
be one sub-interval in which it belongs.
Therefore, if we consider the data set { 0.5, 1.4, 1.3, 2.0, 2.3, 4.5, 5.5}
,
if the assign this data set in accordance with the above the conventions then we will
have: using Open Left Boundary (OLB) convention:
(-infinity, 1]
, we assign the data element 0.5
;
and hence the frequency of this interval is 1
.
(1, 2]
, we assign the data element 1.4, 1.3, 2.0
;
and hence the frequency of this interval (wrt OLB convention) is 3
.
(2, 3]
, we assign the data element 2.3
, and hence
the frequency of this interval (wrt OLB convention) is 1
.
(3, 4]
, we assign no data elements, and hence the frequency of
this interval (wrt OLB convention) is 0
.
(4, 5]
, we assign the data element 4.5
, and hence
the frequency of this interval (wrt OLB convention) is 1
.
(5, infinity)
, we assign the data element 5.5
, and
hence the frequency of this interval (wrt OLB convention) is 1
.
Hence, in this case the array returned corresponding to the frequency table will be
{1, 3, 1, 0, 1, 1}
.
Exception Type | Condition |
---|---|
StatisticsException | Thrown if data set or boundaries intervals are null. |
DataPresentation Class | WebCab.Libraries.Statistics.Statistics Namespace