Statistics / Unit 2: Describing Distributions
2.5 Box Plots
Notes
A box plot displays the five-number summary.
- The box runs from $Q_1$ to $Q_3$ with a line at the median.
- Whiskers extend to the smallest and largest values that are not outliers. Outliers are drawn as separate points.
- Each section (whisker, half of the box) holds about $25\%$ of the data.
- Example: summary 10, 20, 25, 40, 50 has IQR $= 20$, and half the data lie between 20 and 40.
- A median closer to $Q_1$ with a longer right whisker suggests a skewed right distribution.
Practice
A five-number summary is 10, 20, 25, 40, 50. What is the IQR?
IQR $= Q_3 - Q_1 = 40 - 20 = 20$. The range is 40.
About what percent of the data lie between $Q_1$ and the median?
The quartiles split the ordered data into four parts of about $25\%$ each.
In a box plot, the median line is near the left side of the box and the right whisker is much longer than the left. The distribution is most likely:
The long right whisker is the tail, so the shape is skewed right.
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