As a subject matter expert in statistics, I can clarify that the variance is indeed always greater than or equal to the standard deviation. This is because the standard deviation is the square root of the variance. Variance is calculated as the average of the squared differences from the mean, and since squaring any real number results in a non-negative value, the variance is also non-negative. When you take the square root of the variance to get the standard deviation, you're left with a non-negative number that is at most equal to the original variance, but never less. read more >>

Variance cannot be smaller than the standard deviation because the standard deviation is the square root of the variance. The variance of a data set cannot be negative because it is the sum of the squared deviation divided by a positive value.read more >>