it is found that both the experimental data and the theoretical calculations show a large width of a few MeV even in the most well-established ISGMR in $^{208}$Pb. However, it is interesting to note that $E_{ave}$ and $E_{con}$ are rather close within a $0.1\sim 0.2$ MeV difference even when the ISGMR peak has a large width although the scaling energy $E_{sca}$ has a large uncertainty due to the high energy tail of monopole strength, which is always the case in experimental data (and see the theoretical results in the following). Furthermore, from the relation of the energy moments $m_{k+1}m_{k-1}\geq m_{k}^{2}$, one can obtain $E_{sca}\geq E_{ave}\geq E_{con}$. Therefore, the average energy $E_{ave}$ is usually defined as the ISGMR centroid energy and compared between the experimental data and the theoretical calculations. It should be noted that the situation of light nuclei may be quite different from that of medium and heavy nuclei considered in the present work since the strength distribution of ISGMR for light nuclei is usually very fragmented [@Lui01; @Joh03; @You09]. It was suggested in a recent work [@Fur10] that the fragmentation of the strength distribution for the light nuclei might be explained by the clustering effects which are not 