Individuals and Moving Range (I-MR) charts commonly estimate the process standard deviation \(\sigma \) by dividing the span-2 average moving range by the Normal-reference unbiasing constant \(d_2\) . Unlike the bias-corrected sample standard deviation \(S/c_4\) , this estimator depends on ordering through adjacency, so permuting a fixed sample changes the estimate. We formalize this dependence by introducing an independent uniformly random permutation and applying the law of total variance. This gives an exact decomposition of the sampling variance into a values component (the variance of the permutation mean) and an adjacency component (the expected conditional variance over permutations). The permutation mean is order-invariant and equals \(\textrm{GMD}/d_2\) , where \(\textrm{GMD}\) is the sample Gini mean difference. Under i.i.d. Normal sampling, both components admit closed forms. Under the Normal reference, this adjacency component accounts for nearly all of the familiar asymptotic variance inflation of MR(2)/ \(d_2\) relative to \(S/c_4\) . The decomposition itself is not Normal-specific: an appendix gives exact finite-sample expressions for any i.i.d. distribution with finite variance.
