Within-group and overall standard deviation

In some data sets, the 'individuals' can be split into groups.

When the three groups above (A, B and C) are combined, all information about the differences between the groups is lost. The overall variability is also considerably larger than variability within the groups.

The standard deviation of the combined data set is often considerably higher than that of the separate groups.

It is therefore better to separately describe the distributions within the groups than to describe the overall distribution with a single mean and standard deviation.