Oats are often contaminated with rogue kernels of gluten-containing grains like wheat, barley and rye. When producing gluten free oatmeal, possessing an understanding of the consequences of this possibility is prudent, as labeling requirements specify a maximum amount of gluten in terms of ‘parts per million’ (ppm) gluten. Variation in contaminant kernels, along with variation due to measurement itself though, can result in a wide range of possible ppm gluten outcomes in contaminated servings. This research pursues characterization of this variability, highlighting contributors to it, doing so by quantifying distributional outcomes of ppm gluten in wheat kernel contaminated servings. This is done via statistical simulation of wheat kernel contaminated servings, done for a collection of wheat types and incorporating various measurement influences. Results indicate substantial variability in ppm gluten per serving for a given wheat type, as well as between them, with this being compounded by the measurement task itself.