Anomalous data detection with density function I have a very simple exercise from my class for which I need some intuition regarding some quote by the professor. Imagine we have the weights of a number of people and we compute its (non-parametric) density function obtaining: ![enter image description here]( Then the comment by my professor was: > We have a unimodal distribution which we can take as being normal. We detect anomalous data because the probability of an element not being in the normal is less than 0.05. Do you understand this reasoning? To me is totally unclear. Assuming normality is not so bad. But for the other part I think I have to look for an specific part of the graph which I don't know...

Once you assume normality, you have access to the normal distribution numbers. A typical way of defining anomalous data is to declare anything anomalous if its probability of occurring, as defined by the normal distribution, is less than $0.05.$

I'm not quite sure what "Density" means in your problem. I will say that once you assume normality, the original data curve you have here is irrelevant, except for determining the mean and standard deviation of the normal curve you're now going to work with. The standard tables give you the probabilities.

Graphically, on a normal distribution, the standard deviation is the horizontal distance from the peak to either inflection point (up or down from the mean). If you have the raw data, of course, you can simply compute the standard deviation.