New Measures of Spread and a Simpler Formula for the Normal Distribution

Spread can be measured, with some advantages, by measures based on squared pairwise differences instead of measures based on squared differences from the mean.The measures are equal to multiples of the various versions of the standard deviation.Their advantages are that the measure of spread does not depend on a previously defined measure of location, that the spread of a sample and of a population are both square roots of simple averages and are both intuitively reasonable, and that the formula for the normal density is simplified.Computation is not significantly increased.