mean has inconsistent behavior when passed an empty collection

[yurivish]

The mean function does not consistently treat empty iterators, arrays, and general iterables. None of the current behaviors are documented.

The behavior for ranges (AbstractRange{<:Real}) is to return NaN:

julia> using Statistics
julia> mean(1:0)
NaN

The behavior for arrays is to throw an error:

julia> mean([])
ERROR: MethodError: no method matching zero(::Type{Any})

The behavior for general iterables is to throw a different error:

julia> mean(x for x in ())
ERROR: ArgumentError: reducing over an empty collection is not allowed

[jishnub]

Note that these are consistent:

julia> mean(Int[])
NaN

julia> mean(1:0)
NaN

although I'm uncertain if this is accidental rather than the intended result.

[ararslan]

While I agree that the user experience isn't optimal, note that this isn't specific to mean: sum exhibits identical behaviors for these examples. It comes down to whether the correct output type is knowable based on the element type of the input. Range literals always have a real, concrete element type, so zero(T) is defined, which means we can return zero(T) / 0 for the mean. The same is true of Int[], which is why @jishnub's examples match. The same is not true of [], which has element type Any, and thus you get the MethodError noted in the OP. The reasoning behind the ArgumentError for the generator is the same, and that error is arguably more informative for the user than the MethodError.

I'd vote that the documentation for sum and mean both be updated to note that an error is thrown for empty collections unless the element type supports zero (or the init keyword is passed in the case of sum), without specifying what the precise error is.