We perform simultaneous analysis of (1) matter radii, (2) $B(E2; 0^+ rightarrow 2^+ )$ transition probabilities, and (3) excitation energies, $E(2^+)$ and $E(4^+)$, for $^{24-40}$Mg by using the beyond mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric $beta_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{rm m}$, $B(E2)$, and $E(2^+)$ and $E(4^+)$, indicating that it is quite useful for data analysis, particularly for low-lying states. We also discuss the absolute value of the deformation parameter $beta_2$ deduced from measured values of $B(E2)$ and $r_{rm m}$. This framework makes it possible to investigate the effects of $beta_2$ deformation, the change in $beta_2$ due to restoration of rotational symmetry, $beta_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements, and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.
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