  It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit
nonstandard asymptotic rates depending on curvature. Even for distributions
featuring standard asymptotic rates, there are non-Euclidean effects, altering
finite sampling rates up to considerable sample sizes. These effects can be
measured by the variance modulation function proposed by Pennec (2019). Among
others, in view of statistical inference, it is important to bound this
function on intervals of sampling sizes. In a first step into this direction,
for the special case of a K-spider we give such an interval, based only on
folded moments and total probabilities of spider legs and illustrate the method
by simulations.
