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I tend to use histograms of continuous variables adding estimated density curves in order to compare several charts easily. However, I find difficulties when I try to explain what density is and the interpretation of the curve's height to non-statisticians.

The stalwart Wikipedia provide us a good definition:

In probability theory, a probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

Do you think the concept "relative likelihood" would be clear enough for non-statisticians? What is your approach in such situations?

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Attempting to interpret the curve's height is problematic, because the height is meaningless: density curves depict probability by means of area rather than height. (Select any location along the curve. Change the height of the curve there--and only there--to any different value. This does not change any areas, so it gives an equivalent density curve.) Examples: stats.stackexchange.com/questions/14483/…, stats.stackexchange.com/questions/4220/…. –  whuber Jan 14 '13 at 22:48
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