karl pearson
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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, σ = 13.1 Variance, σ2 = 171.6
Variance isn't directly proportional to standard deviation.
Standard deviation is the square root of the variance. Since you stated the variance is 4, the standard deviation is 2.