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...

Example

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 you 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 element 0.5; and hence the frequency of this interval is 1.
• Within the interval [1, 2), we assign the data element 1.4, 1.3; and hence the frequency of this interval (wrt ORB convention) is 2.
• Within the interval [2, 3), we assign the data element 2.0, 2.3; and hence the frequency of this interval (wrt ORB convention) is 2.
• Within the interval [3, 4), we assign no data elements, and hence the frequency of this interval (wrt ORB convention) is 0.
• Within the interval [4, 5), we assign the data element 4.5, and hence the frequency of this interval (wrt ORB convention) is 1.
• Within the interval [5, infinity), we assign the data element 5.5, and hence the frequency of this interval (wrt ORB convention) is 1.

Hence, in this case the series returned corresponding to the frequency table will be {1, 2, 2, 0, 1, 1}.

Reference

StatisticalEngine Class
StatisticalEngine Members