[R] differing behavior of mean(), median() and sd() with na.rm

Ted Harding ted@h@rd|ng @end|ng |rom w|@ndre@@net
Wed Aug 22 18:41:18 CEST 2018

```I think that one can usefully look at this question from the
point of view of what "NaN" and "NA" are abbreviations for
(at any rate, according to the understanding I have adopted
since many years -- maybe over-simplified).

NaN: Mot a Number
NA: Not Available

So NA is typically used for missing values, whereas NaN
represents the reults of numerical calculations which
cannot give a result which is a definite number,

Hence 0/0 is not a number, so NaN; similarly Inf/Inf.

Thus, with your x <- c(NA, NA, NA) mean(x, na.rm=TRUE)
sum(x, na.rm=TRUE) = 0, since the set of values of x
with na.rm=TRUE is empty so the number of elements
in x is 0; hence mean = 0/0 = NaN.

But for median(x, na.rm=TRUE), because there are no available
elements in x with na.rm=TRUE, and the median is found by
searching among available elements for the value which
divides the set of values into two halves, the median
is not available, hence NA.

Best wishes to all,
Ted.

On Wed, 2018-08-22 at 11:24 -0400, Marc Schwartz via R-help wrote:
> Hi,
>
> It might even be worthwhile to review this recent thread on R-Devel:
>
>   https://stat.ethz.ch/pipermail/r-devel/2018-July/076377.html
>
> which touches upon a subtly related topic vis-a-vis NaN handling.
>
> Regards,
>
> Marc Schwartz
>
>
> > On Aug 22, 2018, at 10:55 AM, Bert Gunter <bgunter.4567 using gmail.com> wrote:
> >
> > ... And FWIW (not much, I agree), note that if z = numeric(0) and sum(z) =
> > 0, then mean(z) = NaN makes sense, as length(z) = 0, so dividing by 0 gives
> > NaN. So you can see the sorts of issues you may need to consider.
> >
> > Bert Gunter
> >
> > "The trouble with having an open mind is that people keep coming along and
> > sticking things into it."
> > -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> >
> >
> > On Wed, Aug 22, 2018 at 7:47 AM Bert Gunter <bgunter.4567 using gmail.com> wrote:
> >
> >> Actually, the dissonance is a bit more basic.
> >>
> >> After xxx(...., na.rm=TRUE) with all NA's in ... you have numeric(0). So
> >> what you see is actually:
> >>
> >>> z <- numeric(0)
> >>> mean(z)
> >> [1] NaN
> >>> median(z)
> >> [1] NA
> >>> sd(z)
> >> [1] NA
> >>> sum(z)
> >> [1] 0
> >> etc.
> >>
> >> I imagine that there may be more of these little inconsistencies due to
> >> the organic way R evolved over time. What the conventions should be  can be
> >> purely a matter of personal opinion in the absence of accepted standards.
> >> But I would look to see what accepted standards were, if any, first.
> >>
> >> -- Bert
> >>
> >>
> >> On Wed, Aug 22, 2018 at 7:34 AM Ivan Calandra <calandra using rgzm.de> wrote:
> >>
> >>> Dear useRs,
> >>>
> >>> I have just noticed that when input is only NA with na.rm=TRUE, mean()
> >>> results in NaN, whereas median() and sd() produce NA. Shouldn't it all
> >>> be the same? I think NA makes more sense than NaN in that case.
> >>>
> >>> x <- c(NA, NA, NA) mean(x, na.rm=TRUE) [1] NaN median(x, na.rm=TRUE) [1]
> >>> NAsd(x, na.rm=TRUE) [1] NA
> >>>
> >>> Thanks for any feedback.
> >>>
> >>> Best,
> >>> Ivan
> >>>
> >>> --
> >>> Dr. Ivan Calandra
> >>> TraCEr, laboratory for Traceology and Controlled Experiments
> >>> MONREPOS Archaeological Research Centre and
> >>> Museum for Human Behavioural Evolution
> >>> Schloss Monrepos
> >>> 56567 Neuwied, Germany
> >>> +49 (0) 2631 9772-243
> >>> https://www.researchgate.net/profile/Ivan_Calandra
> >>>
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> >>>
> >>
> >
> > 	[[alternative HTML version deleted]]
> >
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