Averaging rhymes with:
leveraging, disparaging, foraging, leveraging, acknowledging, damaging, disparaging, encouraging, foraging, hemorrhaging, imaging, leveraging, messaging, micromanaging, mismanaging, mortgaging, packaging, pillaging, presaging, ravaging, repackaging, rummaging, salvaging, savaging
Averaging sounds like:
aborigines, abrasions, africanize, africans, afrikaans, aphorisms, appraising, approaching, aversions