Cumulative frequency is the number of observations at or below a given value. Add frequencies successively and plot cumulative totals against upper class boundaries. Include zero at the first lower boundary when appropriate.
Join the plotted values with a smooth increasing curve. Its height must never decrease as you move to the right.
| Reading | Cumulative frequency level for \(n\) observations |
|---|---|
| Median | \(\dfrac{n}{2}\) |
| Lower quartile, \(Q_1\) | \(\dfrac{n}{4}\) |
| Upper quartile, \(Q_3\) | \(\dfrac{3n}{4}\) |
| \(p\)th percentile | \(\dfrac{p}{100}n\) |
Read horizontally from the cumulative-frequency level to the curve, then vertically to the data axis. The interquartile range is \(Q_3-Q_1\). A graph reading is an estimate, so use an accuracy supported by the grid.
To find the number above a threshold, subtract the cumulative frequency at that threshold from the total. To compare groups of different sizes, convert their counts to proportions or percentages.
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