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Lets say I have following data:

Row X Y
1 11 101
2 12 102
3 13 103
4 14 104
5 15 105
6 40 106
7 16 107
8 17 108
9 18 112.7

Now lets say I would want to remove the outliers that are 1.5xIQR above the third quartile or 1.5xIQR below the first. Looking at the data I have

X Y
1. Quartile 13 103
Median 15 105
3. Quartile 17 107
1.5*IQR 6 6

Now only row 6 has an outlier in the X column, because X=40 would be 1.5*IQR above of the 3. quartile of X. When I remove the whole row, then the new stats would look like:

X Y
1. Quartile 12.5 102.5
Median 14.5 104.5
3. Quartile 16.5 106.5
1.5*IQR 6 6

Now with the removal of one row we have a new outlier in row 9 in the Y column, because before the removal it was barely below the cut-off of 113 and now the 3. Quartile dropped to 112.5, which would make 112.7 an outlier.

Is this a wrong approach to outlier removal? How should I proceed from here on?

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    $\begingroup$ Please tell us why you are removing outliers. I have to ask, because the algorithmic approach you are following is rarely useful. $\endgroup$
    – whuber
    Jan 16, 2021 at 18:51
  • $\begingroup$ I wanted to perform a regression on bivariate data. It looked like some values for both parameters had outliers and I was thinking that I should remove those before performing a regression. The reason I had this outliers is not because the measurements were incorrect but because it is a rare occurence. Imagine a survey of the Age of people that just married and then you have cases of 14 year olds or 95 year olds. I wanted to remove these edge cases. $\endgroup$ Jan 17, 2021 at 21:43
  • $\begingroup$ Please add new info as an edit to the Q and not only in comments! Not everybody reads comments ... $\endgroup$ Jan 20, 2021 at 3:44

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