# Interpret density plot

I'm trying to understand this density plot. The X axis is the time between requests. What is the probability of the purple data source having a time between request of 500? What is the probability of the purple data source having a time between requests of 250 - 500? Also, where's a good source to explain how to interpret a density plot?

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## 1 Answer

To get probabilities from probability density functions, you need to integrate.

So for example in your second question "What is the probability of the purple data source having a time between requests of 250 - 500?" you need to find the area between 250 and 500, and you might decide to estimate this by estimating the average density in this region and multiplying by the difference between 500 and 250.

Your first question "What is the probability of the purple data source having a time between request of 500?" is slightly harder if you want the (presumably continuous) time between requests to be exactly 500 seconds. But if you are allowed to take this as meaning any time in the range [499.5,500.5) or [500,501) seconds then you take the same approach: estimate the average density in that period and multiply by the width of the range which is 1 second.

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Thanks. Would I estimate the average density for the region by site? Would it be safe to average by doing (y @ 250 and y @ 500) / 2? – Ron Garrity Sep 13 '11 at 22:14
Thanks for the link too! – Ron Garrity Sep 13 '11 at 22:14
@Ron: On your first question, the average of the end points will do if the line between them is linear (and will nearly do if it is nearly linear). But it would not be so good for example between 0 and 250 where the average density is clearly higher than at either end point. – Henry Sep 13 '11 at 22:32