Deleting Values May Either Increase or Decrease Variance

The impact upon variance when a value is deleted is addressed. It is shown that the cutoff for the deleted value yielding an increase or a decrease in variance is approximately one standard deviation from the mean for a univariate random variable with equally distributed probability on a finite set of elements and for a univariate set of observations. The influence of truncation of the domain for such a discrete random variable and for observations is considered.