Level 2 · Percentiles for the free-shipping threshold

What a percentile says

The p-th percentile is the value that p% of the data falls below. The 25th percentile (P25) of order value is the order a quarter of the way up the sorted list; the 50th is the median; the 90th is where the top 10% begins. In pandas they are all one method:

v = completed["order_value"]
v.quantile(0.25)    # 93.99
v.quantile(0.90)    # 1345.77
v.quantile([0.25, 0.5, 0.75, 0.9])   # several at once, as a Series

Statisticians say quantile for the fraction (0.9) and percentile for the percentage (90th). They are the same idea.

Reading a distribution from four numbers

On Harbor & Pine’s completed orders: P25 $93.99, median $268.94, P75 $659.87, P90 $1,345.77. The gaps grow as you go up: $175 from P25 to the median, $391 to P75, $686 to P90. Gaps that widen toward the top are the signature of a right-skewed column, the same shape the histogram in level 1 showed. A symmetric column would have roughly equal gaps on both sides of the median.

Percentiles also survive outliers. A $11,000 order changes the mean; it does not move P25 or P50 at all.

Shares below a line

The opposite question, “what share of orders is under $75?”, is answered with a comparison and a mean:

(v < 75).mean()    # 0.2097, about 21% of orders

v < 75 gives True or False per order. Python counts True as 1 and False as 0, so the mean is the share of True. This trick works for any condition: (v >= 1000).mean() is the share of orders of $1,000 or more.

For Daniel’s meeting: one order in five is under the current threshold. Raising it to $100 moves every order between $75 and $100 from “ships free” to “pays shipping”, and you can size that group the same way.

Common mistakes

• quantile(25) instead of quantile(0.25). pandas expects a fraction between 0 and 1.
• Reading P90 as a share of the maximum. P90 is a value from the data, not 90% of the largest order.
• Mixing up “below” and “at or below”. v < 75 and v <= 75 differ on orders of exactly $75.00. Match the business rule: free shipping applies at $75 or more, so “pays shipping” is v < 75.
• Counting instead of sharing. (v < 75).sum() is a count of orders. Say which one you report.

Interview note

Expect “what is the difference between the median and the 50th percentile?” (none) and “how would you describe this column without a chart?” A five-number summary (minimum, P25, median, P75, maximum) is the classic answer, and describe() prints it for you.