How should I interpret the height of density plots:
For example in the above plot, peak is at about 0.07 at x=18. Can I infer that about 7% of values are around 18? Can I be more specific than that? There is also a second peak at x=30 with height of 0.02. Would that mean that about 2% of values are around 30?
Edit: The question on Can a probability distribution value exceeding 1 be OK? discusses the probability value of >1 which is not an issue here at all. It also discusses that in relation to naive Bayes classfier which is also not the point here. I want to have, in simple language, the numerical inferences that we can draw from such density curves. The role of area under curve is discussed but my question is specifically what inference can we draw regarding a particular x and y combination that exist on the curve. For example, how can we relate x=30 and y=0.02 on this graph. What statement can we write regarding relation between 30 and 0.02 here. Since densities are for one unit value, can we say that 2% of values occur between 29.5 and 30.5? If that is the case, how do we interpret if values vary from only 0 to 1, as in following plot:
If 100% of values occur between 0 and 1, why any curve is there outside 0 and 1?
There is a flat part here at x=0.1 to x=0.2 where y equals 0.8. It forms a rectangle. How can we find out what proportion of values occur between x=0.1 and x=0.2
(PS: If you find this question interesting/important, please upvote it;)