# Popoviciu's inequality on variances

In probability theory, **Popoviciu's inequality**, named after Tiberiu Popoviciu{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=
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Equality holds precisely when half of the probability is concentrated at each of the two bounds.

Popoviciu's inequality is weaker than the Bhatia–Davis inequality.