Excel Averages Question

Let's say I have 10 different categories. Each category can have a variable number of numeric values. Some might have 12 values. Some might have 8, Some might have 16.

I want to get the average of the values in each category to determine which category has the highest average (and so on down to the lowest).

However, it doesn't seem "fair" that one category is only averaging 8 values, but another is averaging 16.

So, I'd like to even this out, if possible, so that all category averages act like there are only averaging 10 values.

Does that make sense?

How would I go about doing this? Would I, for example, on the category with 16 values, do something like VALUE*(10/16) for all 16 values and then use the result of that formula to calculate the average? For example, if one of the property's value is 4, I'd do 4*(10/16) = 2.5?

That doesn't seem like it would be the ideal way to do it, however. I toyed around with PERCENTILE, but I don't think that would do the trick, either.

Any ideas?