The language used in MATLAB and Octave is designed for vector processing to an extent most developers haven't seen before. MATLAB doesn't mean "Math Laboratory", it means "Matrix Laboratory." Operations on row and column vectors are first-class language elements. You almost never have to manually iterate over an array to compute its statistics -- you'd just say M = mean(A [,dim]) where A is a standalone vector or a column vector of a matrix. In that example, M itself is a vector, if A was a matrix.

MATLAB syntax is ugly but the underlying principles are pretty cool. Well-written code scales automatically on newer hardware, or at least it has the potential to. That's not true in languages where higher-order vectors are built from discrete scalars.

In MATLAB, R, or numpy, it's the difference between `mean(n)` and manually looping. It's not an issue of algorithmic efficiency, it's an issue of lost productivity because they don't even write a function to reuse (all they understand is scripting) they recode the loop every single time they have to sum or take the mean of something.

The point is not computational time; the point is that one could simply call an existing library function rather than hand-coding the loop oneself and risking making an error (a fencepost error, for example).

You missed these key words: "manually iterating"

So looping in a high-level language rather than using vectorized functions.

It's probably more in reference to the layer the work is completed in. I haven't used matlab in years but you can probably sum an array by iterating or you can call a faster more efficient library. You get much greater gains when doing this in higher dimensions. If you can do your operations at a matrix level you get a magnitude improvement in speed in most languages.

I think the concern is over the manual component of it, especially if that set of n is big by human standards. (Say, doublechecking a few hundred entries of some column entry by calculator.)