Level 6 · Which channel's sales are steadier?

Same average, different risk

Imagine two stores that both sell $1,000 a day on average. In the first, most days land between $950 and $1,050. In the second, one day brings $400 and the next $1,800. The averages are equal; the businesses are not. The first can be staffed and stocked from the average; the second needs a buffer, because “average” is rarely what happens.

The standard deviation from level 4 measures exactly that: the typical distance of a day from the average day. Small means predictable, large means volatile.

Daily revenue per channel

The starter builds daily: one row per calendar day, one column per channel. Taking the standard deviation of each column answers Kevin’s question:

daily.mean()   # app 1847.38, marketplace 764.13, web 2766.49
daily.std()    # app 2039.60, marketplace 1190.90, web 2502.56

On every channel the standard deviation is about as large as the mean, or larger. Daily revenue here is driven by a few big business orders and by the November and December peaks, so a “normal day” is hard to define. The box plot shows it: the boxes are short and the dots above them run far.

The coefficient of variation

Web’s standard deviation ($2,503) is the largest, yet web also sells the most. To compare spread between groups of different size, divide the standard deviation by the mean. That ratio is the coefficient of variation (CV):

cv = daily.std() / daily.mean()   # web 0.905, app 1.104, marketplace 1.559

A CV of 0.9 means a typical day is about 90% of the average away from it. Web is the steadiest channel relative to its size; marketplace is the least predictable, with a typical swing of more than one and a half times its average day.

Count the empty days

Marketplace had no completed sale on 295 of the 1,096 days. If you group the orders by day without filling in those days, they disappear: the mean rises to $1,046 and the CV falls to 1.23, which makes the channel look steadier than it is. A day without sales is a real day with revenue 0. The starter’s reindex(...).fillna(0) puts them back.

Common mistakes

• Comparing standard deviations of groups with different means. Use the CV, or compare each group’s spread to its own average.
• Dropping zero days. Grouping orders by day only creates the days that had orders. Build the full calendar first.
• Using the CV on data that can be negative or average near zero. Dividing by a mean close to 0 makes the ratio explode; it is meant for positive quantities like revenue.
• Reading volatility as bad. A channel with big swings may simply sell big items. It still needs more buffer in the plan.