Measures of local variation in a distribution: Expected length of spacings and variances of order statistics

Two measures of variation about the rth order statistic Xr:n are studied: the expected value of the spacing Xr+1:n −Xr:n and the variance of Xr:n. The nature of the dependence of these measures on r, for n fixed, is examined for various classes of distributions. In the case of the variance of Xr:n the situations considered are supplemented by some asymptotic results.