It seems that this issue must have been discussed, but I could not find any reference to it so I open it.

mean behaves inconsistently between array and collection implementations in empty container case. This is especially relevant since missing was introduced into base. Here is a code that shows the problem:

julia> using Statistics

julia> x = Union{Float64,Missing}[missing]
1-element Array{Union{Missing, Float64},1}:
 missing

julia> mean(skipmissing(x))
ERROR: ArgumentError: mean of empty collection undefined: Base.SkipMissing{Array{Union{Missing, Float64},1}}(Union{Missing, Float64}[missing])

julia> mean(collect(skipmissing(x)))
NaN

Maybe a specialized implementation of mean in case when eltype of the collection is specified should be implemented? This is the case of skipmissing which knows that its eltype is Float64. For instance sum handles this case correctly (there is a special mapreduce for this case with skipmissing). Probably more functions in Statistics should be reviewed, but first I would want to understand what is the intention with mean.