Level 3 · Read the price boxes

What a box shows

A boxplot packs a whole distribution into five marks:

• the line inside the box is the median: half the values are below it;
• the bottom and top of the box are the first quartile (Q1) and third quartile (Q3): a quarter of the values are below Q1, a quarter above Q3, so the box holds the middle half;
• the box’s height, Q3 - Q1, is the interquartile range (IQR), a measure of spread that ignores the extremes;
• the whiskers reach out to the furthest values that are still within 1.5 IQR of the box;
• dots beyond the whiskers are values more unusual than that: outliers.

So you read two things from each box: where it sits (how expensive) and how tall it is (how varied).

Drawing it per category

ax = sns.boxplot(data=products, x="category", y="unit_price", order=order, color="#9dc3e6")

x is the grouping column and y the number. Order the boxes by their median so the chart reads as a ranking:

order = products.groupby("category")["unit_price"].median().sort_values(ascending=False).index

The numbers behind the boxes

quantile takes a fraction: 0.25 for Q1, 0.5 for the median, 0.75 for Q3.

g = products.groupby("category")["unit_price"]
g.quantile(0.25)   # Furniture 346.50, Textiles 25.49, ...
g.median()         # Furniture 574.00, Textiles 59.99, ...

Furniture has the highest median, $574, and the tallest box, an IQR of $705: its products run from a $169 table to a $1,659 sofa. Outdoor comes second with a median of $274, but its box is almost as tall ($689.76), stretched by grills, lighting and patio pieces that cost from about $50 to $1,289. Textiles sits at the bottom with a $59.99 median and the most uniform prices, an IQR of $74.50. With only 20 products per category these numbers move a lot when one product changes, so say “of 20 products” when you report them.

Common mistakes

• Calling the middle line the mean. Means don’t appear in a standard boxplot.
• Reading the whiskers as the minimum and maximum. They stop at 1.5 IQR; points beyond are drawn separately.
• Forgetting order=, so the boxes come out in data order and the ranking is lost.
• Using quantile(25) instead of quantile(0.25): quantile takes a fraction between 0 and 1.