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This work presents a complete re-evaluation of the hadronic vacuumpolarisation contributions to the anomalous magnetic moment of the muon,$a_{\mu}^{\rm had, \, VP}$ and the hadronic contributions to the effective QEDcoupling at the mass of the $Z$ boson, $\Delta\alpha_{\rm had}(M_Z^2)$, fromthe combination of $e^+e^-\rightarrow {\rm hadrons}$ cross section data. Focushas been placed on the development of a new data combination method, whichfully incorporates all correlated statistical and systematic uncertainties in abias free approach. All available $e^+e^-\rightarrow {\rm hadrons}$ crosssection data have been analysed and included, where the new data compilationhas yielded the full hadronic $R$-ratio and its covariance matrix in the energyrange $m_{\pi}\leq\sqrt{s}\leq 11.2$ GeV. Using these combined data and pQCDabove that range results in estimates of the hadronic vacuum polarisationcontributions to $g-2$ of the muon of $a_{\mu}^{\rm had, \, LO \, VP} = (693.27\pm 2.46)\times 10^{-10}$ and $a_{\mu}^{\rm had, \, NLO \, VP} = (-9.82 \pm0.04)\times 10^{-10}$. The new estimate for the Standard Model prediction isfound to be $a_{\mu}^{\rm SM} = (11\ 659 \ 182.05 \pm 3.56) \times 10^{-10}$,which is $3.7\sigma$ below the current experimental measurement. The predictionfor the five-flavour hadronic contribution to the QED coupling at the $Z$ bosonmass is $\Delta\alpha_{\rm had}^{(5)}(M_Z^2)= (276.11 \pm 1.11)\times 10^{-4}$,resulting in $\alpha^{-1}(M_Z^2) = 128.946 \pm 0.015$. Detailed comparisonswith results from similar related works are given.

The muon $g-2$ and $\alpha(M_Z^2)$: a new data-based analysis