Vatsal -

Either is going to tell you whether or not you might be in the tail of a distrubition. The box plot takes into consideration that you may not be looking at a 'normal' distribution, right? I haven't used them, but one hint would be if mean and median are very different. People often assume normality for no good reason. (A distribution of means approaches normality with big enough sample size, by the Central Limit Theorem.)

Perhaps the box plot gives you more information. (But z is often useful.)

You should not place too much reliance on either method of finding if the instance in question is far in a tail of the distribution though. Just because a datum is in a tail, does not mean it is wrong. Two 5% tails should contain 10% of the data. Also, a datum could be from another population and still not look out of place in yours. So statistics like those you mention only tell you where to look.

Cheers - Jim

PS - Above I should have said, "Two 5% tails should contain APPROXIMATELY 10% of the data."

I find that Penn State puts a lot of useful information online. Searching on them and "outliers," I got the following, which mentions box plots and scatterplots. I love scatterplots for showing information.

https://newonlinecourses.science.psu.edu/stat504/node/15/

@Mercedes Orú-Lacort

Thanks is there a reference which I cite this method?

@James R Knaub unfortunately I couldn't get you. If I want to know outliers I ultimately need to identify them. I am just looking for one method thats objective.

Thanks

Regards