Histograms, box plots and outliers

The idea

In a histogram the area of each bar is proportional to its frequency, so the height is frequency density: $\frac{\text{frequency}}{\text{class width}}$. A common outlier rule: a value is an outlier if it is more than $1.5 \times \text{IQR}$ beyond the nearer quartile.

1. Find each class width from the class boundaries.
2. Frequency density $=$ frequency $\div$ width; frequency $=$ density $\times$ width.
3. Outlier fences: $Q_1 - 1.5 \times \text{IQR}$ and $Q_3 + 1.5 \times \text{IQR}$.

Watch out A taller bar does not always hold more data: compare areas, not heights.