If I were doing an analysis where I was interested in the means, I would probably use CLM. But in my work, we're often interested in the distribution of values behind each mean. I've become a big fan of the box plot, since it provides so much more information. I don't think it's too intimidating for non-statistical audiences. People can focus on just the mean if they want, and the box and whiskers can just be interpreted as giving a sense of "spread."