Beyond the fact that they are both measures derived from probability density functions, I cannot think of any similarity.
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Formally, the standard deviation is the square root of the variance. The variance is the mean of the squares of the difference between each observation and their mean value. An easier to remember form for variance is: the mean of the squares minus the square of the mean.
Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. A combined variance is a method for estimating variance from several samples, given the size, mean and standard deviation of each. Mathematically, a combined variance is equal to the calculated variance of the set of the data from all samples. See links.
Standard deviation is the variance from the mean of the data.
Labor cost variance means the difference between standard labor cost and actual labor cost.
Favourable variance is that variance which is good for business while unfavourable variance is bad for business