Which of the following numbers can be considered an outlier: 190, 150, 220, 190, 220, 260, 240, 300, 320, 310?

Answer 1

Any number that is greater than Q3+1.5(IQR) or less than Q1-1.5(IQR) is an outlier. The IQR stands for the Interquartile range and is calculated by taking Q3-Q1. From your question, if you put the numbers in order you get the following order: 150, 190, 190, 220, 220, 240, 260, 300, 310, 320, with 190 as Q1 and 300 as Q3. Therefore the IQR is 300-190=110.

On the lower side, we have outliers that are less than Q1-1.5(IQR) which is 190-1.5(110)=25. Since we have no numbers less than 25, we don't have any lower bound outliers.

On the upper side, we have outliers that are greater than Q3+1.5(IQR) which is 300+1.5(110)=465. Wince we have no numbers greater than 465, we have no outliers on the upper side either.

Therefore, none of the numbers are true outliers. However, if you're looking at a dot plot, you can consider the 150 as a faint outlier.

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