Cumulative Frequency
Year 9 📈 Statistics & Probability Draw and interpret cumulative frequency graphs, find quartiles.
📊 Building a Cumulative Frequency Table
Cumulative frequency is the running total of frequencies up to and including each class boundary.
| Height (cm) | Freq | Cumulative Freq |
|---|---|---|
| 150–160 | 4 | 4 |
| 160–170 | 11 | 15 |
| 170–180 | 13 | 28 |
| 180–190 | 7 | 35 |
📈 Cumulative Frequency Graph
Plot cumulative frequency against the upper class boundary and join with a smooth S-shaped curve.
- Plot each (upper boundary, cumulative frequency) point.
- Join with a smooth curve — not straight ruled lines.
- The curve must always go upward (frequencies can only accumulate).
Read off: median at $\frac{n}{2}$, lower quartile at $\frac{n}{4}$, upper quartile at $\frac{3n}{4}$.
📦 Box Plots and the IQR
A box plot (box-and-whisker diagram) displays the five-number summary visually.
⚡ Interquartile Range
$$IQR = Q_3 - Q_1$$ The IQR measures the spread of the middle 50% of the data. It is resistant to outliers, making it more useful than the range for skewed data.
Outlier rule: A value is often classed as an outlier if it falls more than $1.5 \times IQR$ below $Q_1$ or above $Q_3$.
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Cumulative Frequency
🎬
Interactive demonstration available in the Calculator tab!
📊 Cumulative Frequency Tool
Build a cumulative frequency table and estimate quartiles.