About Values to detect Outliers using Box Plot

#1
Hi,

I was wondering if anyone could tell me why, when constructing a box-plot, it is always used that a value of:

Q1-1.5*IQR or lower, defines an outlier
Q1-3.0*IQR or lower, defines a far outlier.

the same with

Q3+1.5*IQR
Q3+3.0*IQR

where
Q1: left side of the box
Q3: right side of the box
IQR: Interquartile range

Is there any reason people uses 1.5 and 3.0? why not 2.0 and 4.0? where do those numbers come from, analytically?

Regards
 
#3
JohnM said:
It was basically a judgment call by John Tukey, the guy who invented boxplots.
It seems like that is the reason...I found an anecdote here: http://exploringdata.cqu.edu.au/box_norm.htm

"Many students are curious about the ‘1.5*IQR Rule’, i.e. why do we use Q1 - 1.5*IQR (or Q3 + 1.5*IQR) as the value for deciding if a data value is classified as an outlier? Paul Velleman, a statistician at Cornell University, was a student of John Tukey, who invented the boxplot and the 1.5*IQR Rule. When he asked Tukey, ‘Why 1.5?’, Tukey answered, ‘Because 1 is too small and 2 is too large."

Thanks anyway :)

If anybody has another reason, please post it.