Definition
Interval
An interval is a numerical step or span between two values or positions.
What it means
To read a scale interval, compare neighbouring labels and find how much the value changes. Do not just count the marks. Equal spaces on a normal linear scale represent equal numerical steps.
Remember it
Interval tells what lies between: one step size or a whole span.
Example
A graph axis is labelled 0, 4, 8, and 12 at equal spaces. Each step increases by 4, so the scale interval is 4. There are four labels but only three intervals from 0 to 12.
Watch for
The interval is not the number of marks. From 0 to 12 in steps of 4, there are three intervals, each with a value of 4.
Common mix-up
When interval means a set of numbers, the notation must also show whether either endpoint belongs to the set.
Exact meaning
An interval is a span between two values or positions. On an ordinary linear scale, the scale interval is the change in value from one marked position to the next equal position. In number-set language, an interval is a continuous stretch of the number line, often described by endpoints and by whether those endpoints are included.