Outlier removal, extremes on both ends A list of numbers and I want to remove the extremes on both ends.
The standard deviation is calculated: 26.3 (rounded to 1 decimal)
Originals
[1.1,87.8,97.2,6.8,8.1,10.8,4.9,8.1,1.9,2.8,1.2,1.2,8.7,5.8,2.1,1.9,1.4,1.2,6.6,1.4,1.3,1.5]

Each Original v.s. Standard deviation
[0.04,3.34,3.7,0.26,0.31,0.41,0.19,0.31,0.07,0.11,0.05,0.05,0.33,0.22,0.08,0.07,0.05,0.05,0.25,0.05,0.05,0.06]

For this case, I want to define the numbers of below criteria as outlier:


*

*either greater than 3 times of standard deviation 

*or small than 0.05 times of standard deviation 



Is this a reasonable way to consider and define outlier?
(This proposed method will be applied to lists of numbers may/not normally distributed.)
Thank you.
 A: Graphical comment. If I've correctly captured your data, here is the boxplot from R. Your title says 'both ends', but I see boxplot 'outliers' only in the upper tail. Do you have any explanation how they might have arisen.
boxplot(x, horizontal=T, col="skyblue2", pch=19)


Only two 'outliers' (no tied ones).
length(boxplot.stats(x)$out)
[1] 2

Even small samples from an exponential distribution often show 'outliers'
in the right tail, which are a natural 'feature' of exponential distributions.
Would be a mistake to remove them from the sample. The population SD below is $\sigma=12.$ The SD of all 22 observations is about 11.4 (already a slight
underestimate of $\sigma.$ The SD of the 20 'non-outliers' is only about 5.2 (serious underestimate).
set.seed(123)
y = rexp(22, 1/12)
boxplot(y, horizontal=T, col="skyblue2", pch=19 )
sd(y)
[1] 11.38477
sd(sort(y)[1:20])
[1] 5.205213


For example, certain members of the Weibull family of distributions and  members of the
Pareto family have even heavier right tails, hence more 'outliers' on the
high side.
A: Outliers are generally defined as:


*

*values lower than Q1 - (1.5 * IQR) on the lower end

*values higher than Q3 + (1.5 * IQR) on the top end


More detail here: https://newonlinecourses.science.psu.edu/stat200/lesson/3/3.2
