# How to use box plots to detect outliers?

Suppose for simplicity that we have Gaussian distributed data with some outliers, whose typical characteristic is getting values that are far from the mean. Suppose my sample size is N.

I was thinking that box plots could handle such a situation, but then I thought that, even without outliers, the region Q1 − 1.5IQR and Q3 + 1.5IQR should contain around 99.3% of observations, i.e. we would have N * 0.7 samples declared as outliers even in the absence of outliers (and even under the hypothetical condition of perfect normality...).

Is there a way to circumvent this behavior? For example, we could check the difference between the observed number of samples outside the whiskers and the expected one N * 0.7. Then declare that there is an outlier outside the whiskers only if this difference is statistically relevant. This way we would have the opportunity to declare that no outliers are present, maybe...

By varying the default threshold of 1.5, maybe we could then also localize the outlier.

Would it make sense such a technique for detecting outliers? Are there techniques for implementing this rough idea?

• Outliers in the box plot appear as dots outside the whiskers. If your data is perfectly normal, then there are no outliers. Maybe your data is slightly skewed to one side, but that is not necessarily accepted as an outlier. Could you please provide some figures or data? Commented Jul 13, 2022 at 15:11
• Thanks for the edit. I do not see why woth normal data we do not have outliers. Whiskers contain data up to q3+1.5×iqr usually. Also with normal samples statistically speaking we will have data outside this range. Commented Jul 13, 2022 at 15:47
• If your data is perfectly normal, then what are the outleris? Commented Jul 13, 2022 at 16:05
• Have a look here, quora.com/… Commented Jul 13, 2022 at 16:10
• That's the point. You say that outliers appears as dots. These dots are there also for normal data, that by construxtion should not have outliers.... Commented Jul 13, 2022 at 17:25