sample() — Random sampling

sample(x, size, replace = FALSE)

Key idea

• sample randomly draws items from a set, each with an equal chance. (e.g. 5 from 100)
• With replace=TRUE, the same item can be drawn more than once.
• With replace=FALSE, each item is drawn at most once. (e.g. 5 distinct cards)
• It is used for random sampling and for imitating experiments (simulation). (e.g. roll a die 1000 times)
• Setting a seed (a fixed starting number) makes the random draw repeat the same way.

Definition

$$\#\text{possible samples}=\{\begin{array}{ll}\left(\genfrac{}{}{0ex}{}{N}{n}\right)& \text{without replacement (order ignored)}\\ N^n& \text{with replacement (order matters)}\end{array}$$

$N$

how many items in the pool

$n$

how many you draw

$\left(\genfrac{}{}{0ex}{}{N}{n}\right)$

ways to draw when order is ignored, no repeats

Where you'd use it

• A raffle sold tickets numbered 1 to 20 and you must draw 6 winners. sample(20, 6) picks 6 different numbers fairly, and setting a seed lets you prove the same draw later.
• You have 50 students and want 10 chosen at random for a survey. sample(50, 10) hands back 10 distinct student numbers, each with an equal chance of being picked.
• To simulate rolling a die 5 times, use sample(6, 5, replace = TRUE) so the same face can repeat; the result might be 3, 1, 6, 6, 2, just like real rolls.

Frequently asked questions

Does sample repeat values?

Not by default. Use replace = TRUE to allow repeats.

Why do results change each run?

It’s random — set.seed() makes it repeatable.