Cumulative frequency
Running total of frequencies. Cumulative frequency curve gives median and quartiles.
Cumulative frequency = sum of frequencies up to a class. Plotted at the upper class boundary, joined with a smooth curve. Read off median (50%), lower quartile (25%), upper quartile (75%); IQR = UQ − LQ.
Worked examples
Frequencies 5, 12, 18, 9, 3; cumulative: 5, 17, 35, 44, 47.
Median: read CF curve at half the total (e.g. 47/2 = 23.5).
IQR = UQ − LQ: read at 75% and 25% of total.
Frequently asked questions
Plotting position?
Upper class boundary — e.g. for 10 ≤ x < 20, plot at 20.
Smooth curve or polygon?
GCSE expects a smooth curve. Frequency polygon (straight lines) is for frequency distributions only.