[doctorsher]

I heavily caution against the feeling that "standard deviation is a simple way to essentially include percentiles." The usefulness of the standard deviation depends on the distributions that you are working with. Heavy tailed distributions appear a fair amount in practice, and the combo of summary statistics mentioned would not do well on those. Also, Madars' comment in this thread is a beautiful example of this: 4 completely different distributions, with identical mean and standard deviation (among other things). Histograms and percentiles, and if necessary their approximations, are more desirable for the above reasons.

[slaymaker1907]

I assume most of the distributions a marketing department would be dealing with are generally normal in which case stddev is a great way to analyze the data. This can be easily verified by just plotting said data and making sure the tails don't look weird.

[im3w1l]

I can't help but idly wonder what humans are doing when they are eyeballing the tails, to see if things look good. Like lets say we wanted to do the eyeball test but automatically. Would the best way be to use an image classifier on the plot? Is there something magic about the plot representation that would make it good even for computers to use?