Level 5 · Read the box plot

Five numbers in one picture

A box plot draws a distribution with five marks:

• the median, the thick line: half the values on each side;
• the box, from Q1 (25th percentile) to Q3 (75th): the middle half of the values, so its height is the IQR from chapter 1;
• the whiskers, reaching to the furthest values within 1.5 × IQR of the box;
• the dots, values beyond the whiskers: the outliers by Tukey’s rule.

g = clean.groupby("segment")["order_value"]
g.quantile([0.25, 0.5, 0.75]).unstack()
#             0.25     0.5      0.75
# business   289.68  682.66  1340.18
# consumer    69.98  189.95   433.99

The chart is these numbers, drawn. That makes it easy to check a reading against the table.

Comparing groups

Box plots earn their place when you put several side by side. Compare three things, in this order:

1. Position: which median is higher? Business orders have a median of $682.66, more than three times the consumer median of $189.95.
2. Overlap: does one box start above the other’s median? The business box starts at $289.68, above the consumer median, so at least 75% of business orders beat a typical consumer order.
3. Width: which box is taller? The business IQR is $1,050.49, the consumer IQR $364.01. Business orders vary far more, so a single “typical business order” is a looser idea.

Order the boxes by median (here consumer, then business) so the eye reads a ranking.

What a box plot hides

A box plot shows nothing about how many values each group has: 7,881 consumer orders and 2,964 business orders get boxes of the same width. It also hides shape inside the box, like two peaks. When the count or the shape matters, put the group sizes in the labels or show a histogram next to it.

The dots need care too. Consumers have 664 orders beyond the whiskers and business accounts 212, because consumers have more orders, not because their data is worse. Outlier dots are a reason to look, as in chapter 1, not a verdict.

Common mistakes

• Reading the top of the box as “most values”. Only 25% of values are above Q3.
• Reading box height as a count. Height is spread. Each box holds the middle half of its group.
• Treating the dots as errors. They are values far from the middle; most are real customers.
• Clipping without saying so. This chart stops at $3,000 and the note says how many orders are not drawn. A cut axis without a note hides the tail.