You want the col moving average function in a column formula. Here's an example for a 5-row moving average on the "# defects" column:
dt = open("$sample_data\Quality Control\Braces.jmp");
dt << New Column( "Defect MA", Numeric, "Continuous", Format( "Best", 12 ),
Formula( Col Moving Average( :name("# defects"), weighting = 1, before = 5 ) )
);
Try running this code and you'll see how it works.
For your table, click on Cols > New columns...
Give the new column an appropriate name, and select Column properties > Formula
Double-click on the blue box labeled no formula, then click the little box in the upper right to maximize the editor.
Paste this formula in: Col Moving Average( :name("# defects"), weighting = 1, before = 5 )
Substitute the column to be averaged for # defects, and set the before parameter to how many rows you want to average.
Click OK and OK and you're all set.