R Functions

Why Are We Programming?

Suppose you want to calculate the average of the first five positive integers, \(\{1, 2, 3, 4, 5\}\). You could directly apply the formula for the mean using nothing but the arithmetic operators you already know.

(1 + 2 + 3 + 4 + 5) / 5
[1] 3

That works fine for five numbers. But what if you had 500 numbers? Or 5 million? Manually typing out every value and dividing by hand simply isn’t realistic. This is exactly why we program: so that a computer can do the repetitive, error-prone parts of a calculation for us, reliably and instantly, no matter how much data we throw at it.

Do: run the code below.

See: it prints 3, the same answer as our hand-calculated formula above.

Explain: let’s break down exactly what happened in that one short line of code.

  • 1:5 creates the sequence of numbers 1, 2, 3, 4, 5.
  • mean(...) takes that sequence and calculates its average.

So mean(1:5) reads almost like English: “the mean of one-through-five.” Instead of writing out the entire formula for a mean every time, we can reuse a small, pre-built piece of code, a function, that already knows how to do that calculation for us.

Practice: Predict, Then Run

Before running the code below, predict what value each line will produce.

1:5
mean(1:5)
sum(1:5)
1:5
[1] 1 2 3 4 5
mean(1:5)
[1] 3
sum(1:5)
[1] 15

1:5 just creates the five numbers themselves. Nothing is calculated yet. mean(1:5) and sum(1:5) both take that same sequence of numbers as an input, but each performs a different operation on it: one averages the values, and the other adds them all together. Same input, different function, different result.

Over the rest of this tutorial, you’ll learn what a function actually is, how to call one, how to change what you feed into it, and how to avoid (and fix) the most common mistakes people make when they’re getting started.

Quick Check

In your own words: why is it useful to have a function like mean() instead of always writing out the full averaging formula by hand?

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