Calculating the average value for some observation in a time bucket, where some buckets may have no observation (resulting in 0/0=nan), finally taking some kind of summary of these ignoring nan values (there is a whole library of functions for this in numpy for example).

NaN and Inf are extremely valuable and useful encodings to represent real things. Particularly signed infinity is wonderful, as functions like exp behave correctly for inf (eg. exp(-inf)=0).