Characterizing temporal inhomogeneities in the interaction patterns of temporal networks is of utmost importance to understand not only the structure of temporal networks but also various collective dynamics taking place in them. Inhomogeneous temporal interaction patterns can be studied both by inhomogeneous interevent times (IETs) and by correlations between IETs, which has often been called correlated bursts (CB). Firstly, we numerically show that the strong CB, depicted by power-law bursty train size distributions, violates the well-established scaling relation between the power-law decaying autocorrelation function and the power-law IET distribution. Secondly, it has been found that the empirical data sets for human activities show power-law bursty train size distributions but almost negligible memory coefficient. For understanding this, we derive an analytic form of the memory coefficient between consecutive IETs as a function of parameters describing IET and bursty train size statistics, to conclude that the memory coefficient might have some limits in quantifying CB. Finally, we study the effects of CB on the spreading in temporal networks to conclude that the positive correlation between consecutive IETs slows down the spreading. We also discuss possible research topics regarding the CB for temporal networks.