I have the following set of numbers, in which I need to determine if there are any outliers: 11, 14, 21, 26, 29, 33, 61.
I graphed them in Desmos (see above), and visually, it appears to me that 61 is an outlier.
I searched online for a mathematical rule to determine whether a number is an outlier, and I found multiple references to the rule that a number is an outlier if it is greater than Q3, or less than Q1, by more than 1.5*(interquartile range).
However, I found two different methods for determining the interquartile range of a data set with an odd number of members:
Method 1 gives the groups (11, 14, 21) and (29, 33, 61), which has medians 14 and 33, for an interquartile range of 19.
Method 2 gives the groups (11, 14, 21, 26) and (26, 29, 33, 61), which has medians 17.5 and 31, for an interquartile range of 13.5.
(Incidentally, the TI-83 calculator uses method 1, and Microsoft Excel uses method 2.)
Getting back to the 'determining outliers' question:
Using method 1 gives 33 + 1.5*19 = 61.5. Since this is greater than 61, by this method, there are no outliers in the data set.
Using method 2 gives 31 + 1.5*13.5 = 51.25. Since this is less than 61, by this method, 61 is an outlier.
So my question is: Is one of these methods considered more correct than the other? Or is the whole 'point' of outliers more intuitive, and less bound by actual formulas, so the right method would be just looking at my graph instead? (If possible, please include links to any authoritative source or reference that you may know of. Thank you.)
EDIT: After reading some of the responses, I think I need to add a bit more context info here. I am reviewing an Algebra textbook meant for middle to high school students, and this is part of a question which appears in that book, specifically in the area of the book where outliers are being taught about. It looks to me like the numbers in this question were specifically chosen to have one be as far away as possible from the rest, while having it not be considered an outlier by the 1.5IQR formula.
I think that this will give students the perspective that outliers are always determined by a rigid formula, without any sort of intuitive 'that point looks far away from the rest' outlook. I am looking for input on whether this a correct / proper outlook to be teaching.
