The Interquartile Range is defined as: $IQR = Q_{3} - Q_{1}$, where $Q_{3}, Q_{1}$ define the lower and upper quartile. What if I want to detect fewer outliers? Can I define custom lower and upper bound such as $IQR = Q_{95} - Q_{5}$ where $Q_{95}, Q_{5}$ define the 95% and 5% quantiles.


$IQR$ is the interquartile range. So, it is not meaningful in this way. You can define the range for outliers like $< Q_1 - 1.5 \times IQR$ or $Q_3 + 1.5\times IQR < $, for example. So, you can control the range by the multiplier of $IQR$ (which is $1.5$ in our example).

Depends on the domain, removing the first and last $5\%$ of data as outliers can be erroneous. For example for $\{1,2,\ldots,50,99, 100\}$, you are removing some related data also. However, you can control the range in the previous method.

  • $\begingroup$ and what if I only want to retrieve the most extreme outliers. How would I approach this? $\endgroup$
    – oezguensi
    Mar 15 '20 at 23:53
  • $\begingroup$ @oezguensi please see the update. $\endgroup$
    – OmG
    Mar 16 '20 at 0:09

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