Level 1 · Why the average order lies

Two kinds of middle

The mean is the sum of the values divided by how many there are. The median is the value in the middle once you sort them: half the values are below it, half above. On a column without extreme values the two are close. On Harbor & Pine’s order values they are far apart:

completed["order_value"].mean()     # 543.30
completed["order_value"].median()   # 268.94

The mean is twice the median. That gap is the first thing to notice about any column.

Why the mean moves and the median doesn’t

The mean uses every value’s size. One order of $11,103 adds as much to the total as forty orders of $270, so a few big orders drag the mean up. The median only cares about order: make the biggest order ten times bigger and the median does not move at all.

Look at the chart. Most orders sit on the left, under $500, and a long thin tail stretches right to $3,000 and beyond. Data shaped like this is called right-skewed. Money, quantities, session lengths and salaries are almost always right-skewed, which is why the question “mean or median?” comes up in nearly every analysis.

(completed["order_value"] < completed["order_value"].mean()).mean()   # 0.70

Seven in ten orders are below the average. A campaign aimed at “customers who spend $540” is aimed at the top 30%.

Which one to report

• Typical customer, typical order, typical salary: the median. It describes a real, middle case.
• Totals and planning: the mean. Revenue = mean order value × number of orders, which is why finance teams use it, and that is correct for their question.
• Both, side by side, whenever the audience might read one as the other. “Average order $543 (half of orders are under $269)” is one honest line.

Common mistakes

• Calling the mean “typical”. On skewed data the mean is pulled toward the tail and describes nobody in particular.
• Dropping big orders to “fix” the mean. They are real customers. Report the median instead of deleting data you don’t like. (Level 5 covers values that really are errors.)
• Comparing means of groups with different tails. A segment with a few huge orders can have a higher mean and a lower median than another. Check both before you say one group “spends more”.

Interview note

“When would you use the median instead of the mean?” is a standard screening question. The answer they want: when the data is skewed or has outliers, because the median is resistant to extreme values. Add a business example like this one and you have a strong answer.