Cumulative frequency and histograms

For large sets of grouped data, cumulative frequency (a running total) lets you estimate the median and quartiles from a curve. Histograms show grouped data with unequal class widths, where area shows frequency.

Key facts

• Cumulative frequency: add up the frequencies as you go.
• Plot at the upper end of each class, then join with a smooth curve.
• Median at n/2, Q1 at n/4, Q3 at 3n/4 (read across, then down).
• Histogram: frequency density = frequency ÷ class width; area = frequency.
• Estimated mean from grouped data uses midpoints.

Worked examples