Alright, honey, interpreting the remainder is like looking at the leftovers after a long meal - it's the amount that doesn't quite fit evenly into the divisor. It's what's left over when you divide one number by another. Think of it as the crumbs at the bottom of the cookie jar - not necessary for the main calculation, but still worth acknowledging.
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Yes the mean can have a remainder but the remainder would normally be either rounded or converted into a fraction.
You incorporate the fractional remainder into the mean. The mean does not have to be a whole number.
If you mean 60 divided by 12 then it is exactly 5 with no remainder.
It means 4 can divide into it evenly with no remainder.