Computer Engineering Commons^™

Computing Variance Under Interval Uncertainty: A New Algorithm And Its Potential Application To Privacy In Statistical Databases, Richard Aló, Mohsen Beheshti, Gang Xiang

Departmental Technical Reports (CS)

Computation of population mean E=(x1+...+xn)/n and population variance V=(x1^2+...+xn^2)/n -E^2 is an important first step in statistical analysis. In many practical situations, we do not know the exact values of the sample quantities xi, we only know the intervals [Xi-Di, Xi+Di] that contain the actual (unknown) values of xi. Different values of xi from these intervals lead, in general, to different value of population variance. It is therefore desirable to compute the range [V]=[V-,V+] of possible values of V.

This problem of computing population variance under interval uncertainty is, in general, NP-hard. It is known that in some reasonable cases, …