why mean not working in Reduce?

Question

There are two examples of function Reduce() in Hadley Wickham's book Advanced R. Both work well.

Reduce(`+`, 1:3) # -> ((1 + 2) + 3)
Reduce(sum, 1:3) # -> sum(sum(1, 2), 3)

However, when using mean in Reduce(), it does not follow the same pattern. The outcome is always the first element of the list.

> Reduce(mean, 1:3)
[1] 1

> Reduce(mean, 4:2)
[1] 4

The two functions sum() and mean() are very similar. Why one works fine with Reduce(), but the other does not? How do I know a if a function behaves normally in Reduce() before it gives incorrect result?

Answer 1

This has to do with the fact that, unlike sum or +, mean expects a single argument (re: a vector of values), and as such cannot be applied in the manner that Reduce operates, namely:

Reduce uses a binary function to successively combine the elements of a given vector and a possibly given initial value.

Take note of the signature of mean:

mean(x, ...)

When you pass multiple values to it, the function will match x to the first value and ignore the rest. For example, when you call Reduce(mean, 1:3), this is more or less what is going on:

mean(1, 2)
#[1] 1

mean(mean(1, 2), 3)
#[1] 1

Compare this with the behavior of sum, which accept a variable number of values:

sum(1, 2)
#[1] 3

sum(sum(1, 2), 3)
#[1] 6