Overload | Description |
---|---|
CFrequencyTableBOR(String,Series,Double[]) | Calculates the cumulative frequency table from below for a discrete data set in accordance with the open right boundary (ORB) convention. |
CFrequencyTableBOR(Series,Double[]) | Calculates the cumulative frequency table from below for a discrete data set in accordance with the open right boundary (ORB) convention. |
CFrequencyTableBOR(SeriesCollection,Double[]) | Calculates the cumulative frequency table from below for a discrete data set in accordance with the open right boundary (ORB) convention. |
Example
Within this example we work through an illustration in which the cumulative frequency table from below 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}
,
if the assign this data set in accordance with the above the conventions then we will
have using Open Right Boundary (ORB) convention:
- Within the interval
(-infinity, 1]
, we assign the data element0.5
; and hence the frequency of this interval is1
. - Within the interval
[1, 2)
, we assign the data element1.4, 1.3
; and hence the frequency of this interval (wrt ORB convention) is2
. - Within the interval
[2, 3)
, we assign the data element2.0, 2.3
; and hence the frequency of this interval (wrt ORB convention) is2
. - Within the interval
[3, 4)
, we assign no data elements, and hence the frequency of this interval (wrt ORB convention) is0
. - Within the interval
[4, 5)
, we assign the data element4.5
, and hence the frequency of this interval (wrt ORB convention) is1
. - Within the interval
[5, infinity)
, we assign the data element5.5
, and hence the frequency of this interval (wrt ORB convention) is1
.
Now in follows that the associated values of the cumulative frequency table are given by:
- Cumulative frequency table up to
1
is:1
- Cumulative frequency table up to
2
is:3
- Cumulative frequency table up to
3
is:5
- Cumulative frequency table up to
4
is:5
- Cumulative frequency table up to
5
is:6
- Cumulative frequency table up to
5
is:7
Hence, for this case the series returned by this methods to represent the cumulative
frequency table would be: {1, 3, 5, 5, 6, 7}
.