I'm just starting to use box & whisker plots
and have a (possibly very naive) question
about using them with skewed distributions.

The box represents skew in the middle of the
distribution nicely by showing the quartile
locations q1, q2, and q3. But the whisker
lengths are defined in terms of IQR=q3-q1, so
the whiskers are the same length for both tails.
This means that the skew in the tails (i.e.
below q1 or above q3) is not represented,
as far as I can see.

I wonder why the same value of IQR is used
to calculate the whiskers at both ends of the distribution.
Instead, I'd think the whisker should be longer on the side
with the longer tail. It would be easy enough to
define the whisker lengths for the two tails
separately, for example in terms of 2*(q2-q1)
and 2*(q3-q2). I'm just wondering why that
isn't routinely done. Have I overlooked
something obvious?

Thanks for your comments,

(By the way, with the distributions I am examining,
it would be very unhelpful to transform the scores
to eliminate the skew, since the skew itself is part
of what's interesting about the dataset.)

I'm just starting to use box & whisker plots
and have a (possibly very naive) question
about using them with skewed distributions.

The box represents skew in the middle of the
distribution nicely by showing the quartile
locations q1, q2, and q3. But the whisker
lengths are defined in terms of IQR=q3-q1, so
the whiskers are the same length for both tails.
This means that the skew in the tails (i.e.
below q1 or above q3) is not represented,
as far as I can see.

I wonder why the same value of IQR is used
to calculate the whiskers at both ends of the distribution.
Instead, I'd think the whisker should be longer on the side
with the longer tail. It would be easy enough to
define the whisker lengths for the two tails
separately, for example in terms of 2*(q2-q1)
and 2*(q3-q2). I'm just wondering why that
isn't routinely done. Have I overlooked
something obvious?

Thanks for your comments,

(By the way, with the distributions I am examining,
it would be very unhelpful to transform the scores
to eliminate the skew, since the skew itself is part
of what's interesting about the dataset.)

The proper drawing will truncate each whisker at
a point where there is still data, and will show
points that may exist beyond the range.

So if there is much skewness, there will be
whiskers of different lengths

The following (from the Wikipedia page on box-plots) expands a
bit on what Rich said.
I had seen that, actually, but thanks for your reply.

* Indicate outliers by open and closed dots. "Extreme" outliers, or
those which lie more than three times the IQR to the left and right from
the first and third quartiles respectively, are indicated by the
presence of an open dot. "Mild" outliers - that is, those observations
which lie more than 1.5 times the IQR from the first and third quartile
but are not also extreme outliers are indicated by the presence of a
closed dot.
What I don't like about this is that I don't think these

Hi Bruce,

The following (from the Wikipedia page on box-plots) expands a
bit on what Rich said.
I had seen that, actually, but thanks for your reply.

* Indicate outliers by open and closed dots. "Extreme" outliers, or
those which lie more than three times the IQR to the left and right from
the first and third quartiles respectively, are indicated by the
presence of an open dot. "Mild" outliers - that is, those observations
which lie more than 1.5 times the IQR from the first and third quartile
but are not also extreme outliers are indicated by the presence of a
closed dot.
What I don't like about this is that I don't think these
extreme values are outliers in my data set, at least not
in the sense of an outlier as a data point generated (primarily)
by some process other than the one I am trying to study.

In general, I am very uncomfortable with any such hard
and fast definitions of outliers. In my area, people often
exclude outliers from their data sets (e.g., before
computation of means, etc). These sorts of statistical
guidelines seem to evolve quickly into statistical
dogma, leading people to exclude a data point
at q3+3.001*IQR but include one at q3+2.999*IRQ.
It seems to me that would probably be a mistake.

Hi Bruce,

The following (from the Wikipedia page on box-plots) expands a
bit on what Rich said.
I had seen that, actually, but thanks for your reply.

* Indicate outliers by open and closed dots. "Extreme" outliers, or
those which lie more than three times the IQR to the left and right from
the first and third quartiles respectively, are indicated by the
presence of an open dot. "Mild" outliers - that is, those observations
which lie more than 1.5 times the IQR from the first and third quartile
but are not also extreme outliers are indicated by the presence of a
closed dot.
What I don't like about this is that I don't think these
extreme values are outliers in my data set, at least not
in the sense of an outlier as a data point generated (primarily)
by some process other than the one I am trying to study.

In general, I am very uncomfortable with any such hard
and fast definitions of outliers. In my area, people often
exclude outliers from their data sets (e.g., before
computation of means, etc). These sorts of statistical
guidelines seem to evolve quickly into statistical
dogma, leading people to exclude a data point
at q3+3.001*IQR but include one at q3+2.999*IRQ.
It seems to me that would probably be a mistake.