Box Plots and Whisker Plots

Constructing a box plot

Step 1 — Sort data: {2, 5, 7, 8, 11, 12, 15, 18, 22, 25, 30}. $n = 11$.

Step 2 — Find the five-number summary:

• Min = 2
• Q1 (25th percentile) = 7 (median of lower half)
• Q2 (median) = 12 (middle value)
• Q3 (75th percentile) = 22 (median of upper half)
• Max = 30

Step 3 — IQR: $Q3 - Q1 = 22 - 7 = 15$

Step 4 — Fences (outlier boundaries):

• Lower fence: $Q1 - 1.5 \times IQR = 7 - 22.5 = -15.5$
• Upper fence: $Q3 + 1.5 \times IQR = 22 + 22.5 = 44.5$

Step 5 — Outliers: Any values below $-15.5$ or above $44.5$. None in this dataset.

Step 6 — Whiskers: Extend to the most extreme non-outlier values. Left whisker to 2, right whisker to 30.

Reading a box plot

• Box = middle 50% of data (IQR)
• Line in box = median
• Whiskers = range of non-outlier data
• Dots beyond whiskers = outliers

Try it in the visualization

The box plot builds step by step. Data points animate into sorted order, quartiles are computed, and the box forms around Q1–Q3.