Can the sample variance ever be a negative number?
No
If not, why not?
Because it is the sum of squares of numbers divided by 1 less than the
number of numbers. Squares are never negative, so you could never have
the sum of squares being negative, and then when you divided by 1 less
than the number of numbers you could never get a negative number.
Can the sample variance ever be zero?
Yes
If so, for what types of data?
When all the numbers in the data set are the same, (which
means they do not vary at all, so it would be logical that
their variance would be zero).
Edwin