How to Traverse Data with Apply Functions in R

By Andrie de Vries, Joris Meys

R has a powerful suite of functions that allows you to apply a function repeatedly over the elements of a list. The interesting and crucial thing about this is that it happens without an explicit loop.

Because this is such a useful concept, you’ll come across quite a few different flavors of functions in the apply family of functions. The specific flavor of apply() depends on the structure of data that you want to traverse:

  • Array or matrix: Use the apply() function. This traverses either the rows or columns of a matrix, applies a function to each resulting vector, and returns a vector of summarized results.

  • List: Use the lapply() function to traverse a list, apply a function to each element, and return a list of the results. Sometimes it’s possible to simplify the resulting list into a matrix or vector. This is what the sapply() function does.


The ability to apply a function over the elements of a list is one of the distinguishing features of the functional programming style as opposed to an imperative programming style. In the imperative style, you use loops, but in the functional programming style you apply functions. R has a variety of apply-type functions, including apply(), lapply(), and sapply().