The shape of a distribution

The mean and standard deviation hold no information about the shape of a distribution, other than its centre and spread.

Many different distributions have the same mean and standard deviation.

Clusters, outliers and skewness are important features of a data set and should influence the analysis that you perform and the conclusions that you reach. In particular, if you ignore outliers or clusters, you could easily reach the wrong conclusions.

It is therefore essential that you look at a graphical display of a distribution before summarising with a mean and standard deviation.