histtable() — Histogram (from a table)

Histogram from a table — the bar’s AREA equals its frequency.

height = frequency / width

Key idea

• This builds a histogram from a table of counts (a frequency table) where bins can have unequal widths.
• When widths differ, the AREA of each bar (not its height) shows the count, called the frequency.
• Height is the frequency density: the frequency divided by the bin width. (e.g. 12 / 6 = 2)
• Using density keeps a wide bin from looking falsely tall and fooling the eye. (e.g. 30 over width 15 -> height 2)
• To get a frequency back, multiply a bar's height by its width. (e.g. height 4 x width 5 = 20)

Definition

$$\text{frequency}=\text{width}\times \text{height}\Rightarrow \text{height}=\frac{\text{frequency}}{\text{width}}$$

$\text{frequency}$

the count in the class

$\text{width}$

the class width

$\text{height}$

the frequency density

$$\text{height}=\frac{14}{20}=0.7,\text{area}=20\times 0.7=14$$

In plain words

A wide bin is not automatically taller — what counts is the area. Spread the frequency over the bin's width to get its height.

Where you'd use it

• Ages are grouped into uneven bands: 0–10: 4, 10–20: 9, 20–40: 14, 40–60: 8. The 20–40 band has the most people (14) but its width is 20, so its height is only 14/20 = 0.7 — shorter than the 10–20 bar (height 0.9), because area, not height, shows the count.
• Income brackets like 0–25k, 25–50k, 50–100k have different widths; using frequency density keeps the wide top bracket from looking falsely huge.
• Exam scores in equal 10-point bands behave normally — equal widths mean the heights are just the counts ÷ 10, so the shape is unchanged.

Frequently asked questions

What goes into the table?

Class intervals (or their midpoints) and the matching frequencies.