Cumulative frequency is a running total of the frequencies. For each class boundary it answers one question: how many values are less than or equal to this value? You build it by adding each class frequency on to the total so far.

Take three classes with frequencies 4, 10 and 6. Keep a running total down the table:

The final cumulative frequency, 20, is the total number of values n.

The cumulative frequency curve

Plot each cumulative frequency against the upper class boundary of its class and join the points. The result is a smooth, rising, S-shaped curve called an ogive. From it you can read off the key summary values: go up to the curve from the right cumulative-frequency height, then across.

• The median sits at \tfrac{n}{2} of the total.
• The lower quartile Q_1 sits at \tfrac{n}{4}.
• The upper quartile Q_3 sits at \tfrac{3n}{4}.