Mean / Variance allowed in interval scale?

Hi all,
I wonder if it's allowed to compute a mean in an interval scale (i.e.
no absolute zero, take degrees in Fahrenheit or Celsius but not Kelvin
as example). I once read that only + and - are allowed operations in
interval scales. But for computing a mean I need to divide by the
number of items. Maybe the point is that multiplying and dividing is
allowed in interval scale if one does it with scalars (thinking of a
vector space). But a typical textbook phrase is: "It does not make
sense to state that 10 degrees F is double as warm as 5 degrees F but
with Kelvin it is right." So even scalar multiplication is not
meaningful in interval scale.

Does anybody know a solution to this?

thx in advance
psj

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