Does it make sense to look at a scatterplot of means versus standard deviations in terms of looking for outliers or changepoints? So the mean is on the x-axis and the standard deviation is on the y-axis. We would get a clusters of data indicating similar data (relatively same mean and standard deviation). Note that I don't know the sample size or individual observations from which these means and standard deviations were computed from.
I assume you're examining data from a continuous outcome that is somehow clustered at a group level. An example of this might be inflation adjusted profit margins over years for several restaurants in the same zipcode, though I'm curious what your data represent.
There is nothing fundamentally instructive about the relationship between means and standard deviations unless part of a prespecified analysis plan. Instead, you can display summaries about the spread of data at each aggregate level using a box-and-whiskers plot, or a forest plot with 95% confidence intervals for the observed mean values.