Yes
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The mean would be negative, but standard deviation is always positive.
That is false. A negative times a negative is always a positive. Since absolute numbers are always positive if you make it negative that is not correct.
This is not strictly true, because an absolute value, and hence the product of two absolute values can be zero. It is, therefore true to say that the product of two absolute values is always non-negative. An absolute value of a number is, by definition, non-negative. And by the definition of multiplication, the product of two non-negative numbers in non-negative.
No. A negative plus a negative will always be negative. Adding negatives just makes them more negative, just like adding positives makes them more positive.If you're thinking of multiplication, then the answer is yes. Like signs result in positive values. Opposite signs result in negative values.
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