The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This interpretation leads to a geometric visualization of the sample SD, and a more elementary explanation as to why the denominator in the sample variance is one less than the sample size.