Calculates the cumulative frequency table from above for a discrete data set in accordance with the open right boundary (ORB) convention.
Before this method is called you are required to set the discrete data set and the boundaries interval using SetDataSet and SetBoundariesIntervals.
Within this example we work through an illustration in which the cumulative frequency table from above using the open right boundary convention is evaluated.
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 right 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}
,
and if we assign this data set in accordance with the Open Right Boundary (ORB) convention
then we will have:
(-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
;
and hence the frequency of this interval (wrt ORB convention) is 2
.
[2, 3)
, we assign the data element 2.0, 2.3
, and hence
the frequency of this interval (wrt ORB convention) is 2
.
[3, 4)
, we assign no data elements, and hence the frequency of
this interval (wrt ORB convention) is 0
.
[4, 5)
, we assign the data element 4.5
, and hence
the frequency of this interval (wrt ORB convention) is 1
.
[5, infinity)
, we assign the data element 5.5
, and
hence the frequency of this interval (wrt ORB convention) is 1
.
Now in follows that the associated values of the cumulative frequency table are given by:
-infinity
is: 1 + 1 + 0 + 2 + 2 + 1 = 7
1
is: 1 + 0 + 2 + 2 + 1 = 6
2
is: 0 + 2 + 2 + 1 = 5
3
is: 2 + 2 + 1 = 5
4
is: 2 + 1 = 3
5
is: 1
Hence, for this case the array returned by this methods to represent the cumulative
frequency table would be: {7, 6, 5, 5, 3, 1}
.
Exception Type | Condition |
---|---|
StatisticsException | Thrown if the input data are not given. |
DataPresentation Class | Statistics Namespace