How does a systematic time-dependence of the diffusion coefficient <i>D</i>(<i>t</i>) affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this question <i>via</i> studying the characteristics of a set of standard statistical quantifiers relevant to single-particle-tracking (SPT) experiments. We examine, for instance, how the behavior of the ensemble- and time-averaged mean-squared displacements-denoted as the standard MSD 〈<i>x</i><sup>2</sup>(<i>Δ</i>)〉 and TAMSD quantifiers-of FBM featuring (where <i>H</i> is the Hurst exponent and <i>Δ</i> is the [lag] time) changes in the presence of a power-law deterministically varying diffusivity <i>D</i><sub><i>α</i></sub>(<i>t</i>) ∝ <i>t</i><sup><i>α</i>-1</sup>-germane to the process of scaled Brownian motion (SBM)-determining the strength of fractional Gaussian noise. The resulting compound "scaled-fractional" Brownian motion or FBM-SBM is found to be nonergodic, with 〈<i>x</i><sup>2</sup>(<i>Δ</i>)〉 ∝ <i>Δ</i><sup><i>α</i>+2<i>H</i>-1</sup> and . We also detect a stalling behavior of the MSDs for very subdiffusive SBM and FBM, when <i>α</i> + 2<i>H</i> - 1 < 0. The distribution of particle displacements for FBM-SBM remains Gaussian, as that for the parent processes of FBM and SBM, in the entire region of scaling exponents (0 < <i>α</i> < 2 and 0 < <i>H</i> < 1). The FBM-SBM process is aging in a manner similar to SBM. The velocity autocorrelation function (ACF) of particle increments of FBM-SBM exhibits a dip when the parent FBM process is subdiffusive. Both for sub- and superdiffusive FBM contributions to the FBM-SBM process, the SBM exponent affects the long-time decay exponent of the ACF. Applications of the FBM-SBM-amalgamated process to the analysis of SPT data are discussed. A comparative tabulated overview of recent experimental (mainly SPT) and computational datasets amenable for interpretation in terms of FBM-, SBM-, and FBM-SBM-like models of diffusion culminates the presentation. The statistical aspects o...