Yes, the variance of a data set is the square of the standard deviation (sigma) of the set. This means that the variance is always a positive number, even though the data might have a negative sigma value.
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Standard deviation is the square root of the variance.
No, you have it backwards, the standard deviation is the square root of the variance, so the variance is the standard deviation squared. Usually you find the variance first, as it is the average sum of squares of the distribution, and then find the standard deviation by squaring it.
Standard deviation is the square root of the variance. Since you stated the variance is 4, the standard deviation is 2.
The variance
Standard Deviation = (principal value of) the square root of Variance. So SD = 10.