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We present measurements of the cross section for anti-neutrinocharged-current quasielastic-like scattering on hydrocarbon using the mediumenergy (ME) NuMI wide-band neutrino beam peaking at $<E_{\nu}>\sim 6$ GeV. Thecross section measurements are presented as a function of the longitudinalmomentum ($p_{||}$) and transverse momentum ($p_{T}$) of the final state muon.This work complements our previously reported high statistics measurement inthe neutrino channel and extends the previous anti-neutrino measurement made inthe low energy (LE) beam at neutrino energy($<E_{\nu}>$) $\sim$ 3.5 GeV to$p_{T}$ of 2.5 GeV/c.  Current theoretical models do not completely describe the data in thispreviously unexplored high $p_{T}$ region. The single differential crosssection as a function of four momentum transfer ($Q^{2}_{QE}$) now extends to 4GeV$^2$ with high statistics. The cross section as a function of $Q^{2}_{QE}$shows that the tuned simulations developed by the MINERvA collaboration thatagreed well with the low energy beam measurements do not agree as well with themedium energy beam measurements. Newer neutrino interaction models such as theGENIE 3 tunes are better able to simulate the high $Q^{2}_{QE}$.

High-Statistics Measurement of Antineutrino Quasielastic-like scattering at $E_\nu \sim$ 6~GeV on a Hydrocarbon Target