Level 1 · Order value bands

Shape before summary

Last chapter you saw that the mean order ($543) is twice the median ($269). That gap tells you the column is right-skewed, but not what the shape looks like. A distribution answers “how many values are there at each size?”, and to see it you group the values into ranges, called bins or bands, and count each one.

pandas measures the lopsidedness directly:

completed["order_value"].skew()   # 3.95

A skew of 0 means symmetric. Above 1 is strongly right-skewed: most values are small, with a long tail of big ones. Order values sit at almost 4.

Cutting values into bands

pd.cut assigns each value to a band you define:

bins = [0, 100, 250, 500, 1000, 2500, float("inf")]
labels = ["under $100", "$100-250", "$250-500", "$500-1,000", "$1,000-2,500", "$2,500+"]
bands = pd.cut(completed["order_value"], bins=bins, labels=labels)
bands.value_counts(sort=False)

Each band includes its right edge: an order of exactly $100.00 lands in “under $100”. A value outside every band (here the 4 orders worth $0 or less) gets NaN and is left out of the counts. sort=False keeps the bands in their natural order instead of sorting by count.

Uneven bands on purpose

The bands here get wider as values grow: $100, $150, $250, $500, $1,500 wide. On a skewed column that is the point. Equal $500 bands would put two thirds of orders in the first band and leave the top bands with a handful each. Wider bands where the data is thin keep every band meaningful.

Orders versus revenue

The chart puts two distributions side by side. Orders pile up on the left: a quarter of them are under $100. Revenue piles up on the right: those small baskets bring in 2% of sales, while orders above $1,000 (15% of orders) bring in more than half. Both are true, and they answer different questions. “Where are most customers?” is the orders view. “Where is the money?” is the revenue view. A good analyst shows Jordan both before he sets offer thresholds.

Common mistakes

• Forgetting the edges. pd.cut includes the right edge and excludes the left. A first edge of 0 drops zero and negative values; check how many NaN you get with bands.isna().sum().
• Sorting by count. value_counts() sorts the biggest band first by default. On order values the bands happen to shrink in order, so you wouldn’t notice; on most columns it scrambles the distribution. Say sort=False and the bands stay in their own order.
• Equal-width bands on skewed data. Most bands end up nearly empty and one band holds most of the data. Use bands that match how the business talks, or quantiles with pd.qcut.