Constructing Cumulative-Frequency Graphs
Cumulative frequency is a running total. At an upper boundary it tells you how many observations lie below that boundary.
Exact points, two different joins
top: upper boundary · bottom: cumulative frequency
“Draw a cumulative-frequency curve” means a smooth increasing curve. Straight segments are a polygon.
Build the running-total table
Start at zero at the lowest boundary. Then add each class frequency to everything already counted.
Worked example
From frequencies to cumulative frequencies
Frequencies give
.
The final value 250 is a useful check: it must equal the total frequency.
Common mistake
Plot at upper boundaries, then use the requested join
- Recover true boundaries. For lengths recorded to the nearest centimetre, 5–9 ends at 9.5 and the full range begins at 4.5.
- Plot each total at its upper boundary. Do not use class midpoints. The first example point is .
- Include the starting zero. Add so the graph covers the complete range.
- Read the exact wording. A cumulative-frequency curve needs a smooth increasing curve. A cumulative-frequency polygon uses straight segments. Exact points agree, but estimates between them can differ.
The graph may rise or flatten, but it must never fall: a running total cannot decrease.
Now you try
Lengths are measured to the nearest centimetre.
Draw a cumulative-frequency graph.
Show worked answer
Plot on labelled linear axes. Join all points with a smooth increasing curve, not straight segments.