Adding frequency count cells to a histogram

One reason for editing histograms is to add frequency count cells without greatly increasing the number of steps.


Editing a histogram with a dense frequency count

The changes you make to histograms vary, depending on whether the values represent a dense or sparse frequency count. To add a frequency cell for a given column value, check the column value just less than the value for the new cell. If the next-lesser value is as close as possible to the value to be added, then you can determine the frequency count.

If the next-lesser column value changed is as close as possible to the frequency count value, you can easily extract the frequency count cell.

For example, if a column contains at least one 19 and many 20s, and the histogram uses a single cell to represent all the values greater than 17 and less than or equal to 22, optdiag output shows the following information for the cell:

Step     Weight                Value
... 
4        0.100000000    <=     17
5        0.400000000    <=     22
... 

Altering this histogram to place the value 20 on its own step requires adding two steps, as shown here:

... 
4     0.100000000    <=     17
5     0.050000000    <=     19
6     0.300000000    <=     20
7     0.050000000    <=     22
... 

In the altered histogram above, step 5 represents all values greater than 17 and less than or equal to 19. The sum of the weights of steps 5, 6, and 7 in the modified histogram equals the original weight value for step 5.


Editing a histogram with a sparse frequency count

If the column has no values greater than 17 and less than 20, use the representation for a sparse frequency count. Here are the original histogram steps:

Step     Weight                Value
... 
4        0.100000000    <=     17
5        0.400000000    <=     22
... 

The following example shows the zero-weight step, step 5, required for a sparse frequency count:

... 
4     0.100000000    <=    17
5     0.000000000    <     20
6     0.350000000    =     20
7     0.050000000    <=    22
...

The operator for step 5 must be <. Step 6 must specify the weight for the value 20, and its operator must be =.