hist() — Histogram

hist(x, breaks)

Key idea

• A histogram groups continuous numbers into ranges called bins and draws a bar for each.
• The height of each bar shows how many values fall inside that bin. (e.g. bin 10-20 has 7 values)
• Bars touch with no gaps because the data flows smoothly, not in separate categories.
• It reveals the overall shape, such as where most values cluster. (e.g. ages 20-30 most common)
• Wider or narrower bins change how smooth or detailed the picture looks. (e.g. bins of width 5 vs 10)

Definition

$$k=\lceil {\log }_{2}n\rceil +1(\text{number of bins, Sturges rule})$$

$n$

how many data points

$k$

a suggested number of bins

$\lceil \cdot \rceil$

round up to a whole number

Where you'd use it

• You have 200 exam scores and want to see their shape. A hist sorts them into buckets like 50–60, 60–70, and so on; a tall bar over 70–80 tells you most students scored in the seventies, with shorter bars at the extremes.
• Plot 500 people’s heights and the histogram piles into a single hump centred near 170 cm, confirming heights cluster around the middle in a bell-like shape.
• Graph 300 clinic waiting times and you might see a tall stack of bars at 0–20 minutes with a long thin tail stretching past 60 — a clear sign that a few rare long waits drag out the right side.

Frequently asked questions

How many bins should I use?

Enough to show the shape without noise — try a few. The bin width changes the story.

Histogram or bar chart?

Histogram for continuous numbers (bars touch); bar chart for categories.