Line Graphs — Revision Notes

⚡ 30-Second Revision

Revision checked 17 October 2026.

Point = level; interval = change.
Rate = change/time.
Percent change uses the initial base.
Subtract cumulative values.
Interpolation and causation need extra justification.

2-Minute Revision

A rise of 30 across three years is slower on average than a rise of 15 in one year. Compare paired series at the same time. Equal vertical gains can have different percentage gains because starting bases differ. A flat segment means the displayed value is unchanged; its meaning depends on the variable. Do not add cumulative endpoints as independent production.

5-Minute Revision

Original drill: Series A has 50, 60 and 72; B has 40, 65 and 70 over three equally spaced years. A’s gains are 10 and 12, both 20 percent. B leads only in the middle year, despite having the larger first increase. A’s observed mean is 182/3, which is a mean of recorded values, not automatically a continuous-time average. Explain why the line crossings do not identify an exact date without a linear interpolation convention.

Vyyuha Quick Recall

LINES: Legend; Intervals; Numerical scale; Endpoint base; Series meaning.