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No. Variance is always positive and so the sum of variances must also be positive.
Favourable variance is that variance which is good for business while unfavourable variance is bad for business
The variance is always positive. The variance is not directly related to the sign (nor magnitude) of the mean.
The SD is the (positive) square root of the variance.
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.