Variance　changepoints　in　economics,　finance,　biomedicine,　oceanography,　etc.　are　frequent　and　significant.　To　better　detect　these　changepoints,　we　propose　a　new　technique　for　constructing　confidence　intervals　for　the　variances　of　a　noisy　sequence　with　multiple　changepoints　by　combining　bootstrapping　with　the　weighted　sequential　binary　segmentation　(WSBS)　algorithm　and　the　Bayesian　information　criterion　(BIC).　The　intensity　score　obtained　from　the　bootstrap　replications　is　introduced　to　reflect　the　possibility　that　each　location　is,　or　is　close　to,　one　of　the　changepoints.　On　this　basis,　a　new　changepoint　estimation　is　proposed,　and　its　asymptotic　properties　are　derived.　The　simulated　results　show　that　the　proposed　method　has　superior　performance　in　comparison　with　the　state-of-the-art　segmentation　methods.　Finally,　the　method　is　applied　to　weekly　stock　prices,　oceanographic　data,　DNA　copy　number　data　and　traffic　flow　data.