rnorm() — Random normal samples

Pulls out random numbers that follow the bell-shaped pattern.

rnorm(n, mean = 0, sd = 1)

Key idea

• rnorm draws n random numbers from a normal distribution with a given mean (centre) and sd (spread). (e.g. rnorm(5, 180, 10))
• Each run gives different numbers because the draws are random.
• Setting a seed first — a fixed starting number — makes the same random values appear every time.
• With many draws, the average of your sample lands close to the true mean. (e.g. n = 1000 -> mean ~ 180)
• It is useful for simulations and for seeing how randomness behaves.

Definition

$$X_1,\dots ,X_n\stackrel{\text{iid}}{\sim }N(\mu ,{\sigma }^2)$$

$n$

how many values to draw

$\mu$

the mean

$\sigma$

the standard deviation

$N(\mu ,{\sigma }^2)$

a normal distribution

$$X_i\sim N(180,10^2)\Rightarrow \bar{x}\approx 180,s\approx 10$$

In plain words

Like a bag full of heights that bunch up around the middle. You reach in and grab n of them without looking. The seed — a starting number — makes sure you grab the same ones each time, so the result can be repeated.

Where you'd use it

• You want a pretend class of 30 test scores to practise on. rnorm(30, 75, 8) invents 30 numbers centred near 75, most landing between about 59 and 91, so you get realistic-looking scores without any real data.
• To model tiny measurement errors in an experiment, draw noise with rnorm(100, 0, 0.5). You get 100 small wobbles averaging near 0, mimicking the random slip in each reading.
• Generate 200 fake heights with rnorm(200, 170, 7) to test other functions; their average comes out close to 170 cm, and using the same seed lets a friend reproduce the exact same 200 numbers.

Frequently asked questions

Why do I get different numbers every run?

rnorm draws random samples. Call set.seed(n) first to make them reproducible.

How do I set the centre and spread?

rnorm(n, mean, sd) — the 2nd/3rd args. sd is the standard deviation, not the variance.