If zero is in your number set do you count it when figuring the mean
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The short answer is yes.
The long answer is yes, assuming that the zeros are true
numbers, not just blanks or missings that were filled in as zero by
some software tool (many times software packages have options that
treat missing values as zero).
If the zero is a valid instance, count it.
Example:
Rainfall in inches this week: 0, 1, 0, 0, 1, 0, 5. The average
is 1 (7/7).
Height of adults in inches: 72, 68, 60, 0, 62, 65. The average
is 65.4 (327/5). The 0 was a missing number, clearly not a valid
height.