In column A there is a series of numbers; for each number, in column B is its
associated category. For each grouping of adjacent rows with identical
category, I want a formula in column C that will return the average of the
numbers for that grouping. It could be, say, at the top of each grouping;
for other cells the formula would return a blank. Not all groupings are
equal in height. The same category may appear in more than one grouping; in
this case, the formula will return the average for each separated grouping.

Can I make a formula that will yield this result?