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I have a polygon shapefile which I have imported into QGIS, however it does not display X Y coordinates. Is there a way that I can identify the coordinate for the centroid of the polygon and display this in the attribute table?

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    It's certainly possible, but first you need to identify the meaning of "centroid", since there are several options, and not all of them are "inside" the polygon. – Vince Nov 23 '16 at 12:00
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The QGIS field calculator can do it with these built-in functions:

 x( centroid(  $geometry ))
 y( centroid(  $geometry ))

Make sure to create a new field of type real, with an accuracy of 8. You can even use a virtual field to avoid changing the datasource.

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