Average vs median: which one to report, and why the average misleads with money

“A typical order is worth €61” sounds like a fair summary. On the Meridian practice marketplace it isn’t: half of paid orders are below €43.96. The mean of €60.92 is the right number for estimating total sales, but a few large orders pull it up and hide how spread out order values are. Describe a typical order with the median, and look at the distribution before planning around either number.

Short version: for money, time and counts — anything skewed to the right — report the median as the “typical” value and use the mean for totals, expected values and other questions where each value should contribute (mean × count = total). Put a high percentile next to them to show the spread.

The numbers

Paid orders on Meridian, 31 August – 22 September 2026:

The average is 39% above the median. Here, the distribution has many small orders and a long tail of large ones. A mean above the median is a clue to inspect the distribution, not by itself proof of its shape.

The gap changes by segment

Two lessons. First, the overall average mixes very different categories; a change in the mix (more Electronics during a promo) moves the average even if nothing changed within any category. Second, the order of categories is the same by mean and by median here — but that is something to check, not assume.

When to use which

• Median — the typical case: typical basket, typical delivery time, typical session length, typical salary. Robust to a few extreme values.
• Mean (average) — when you need totals or unit economics: revenue = orders × average order value. Also for roughly symmetric data such as many physical measurements.
• Percentiles (p90, p95) — the experience of the worst-served customers: slow deliveries, long waits. Service levels are usually set on a high percentile, not on the average.
• Trimmed mean — a compromise when a handful of genuine extreme values would dominate. An obvious error, such as a €99,999 test order, should be traced and excluded for its own reason, not trimmed away.

Traps

1. Averaging averages. The average of six category averages is not the overall average; weight by the number of orders or compute from the rows.
2. Averaging medians. Group medians and group sizes generally do not contain enough information to recover the overall median; compute it from the underlying values.
3. Comparing averages across a mix change. A higher average can come from a shift in which customers bought, not from customers buying more. See Simpson’s paradox.
4. Outliers that are errors. Before trimming, check: a €542 order may be real; a €54,200 order deserves a source-record and unit check, not automatic removal.

In SQL

SELECT AVG(items_total_eur)                        AS mean_eur,
       MEDIAN(items_total_eur)                     AS median_eur,   -- DuckDB; PostgreSQL: PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY …)
       QUANTILE_CONT(items_total_eur, 0.9)         AS p90_eur,      -- PostgreSQL: PERCENTILE_CONT(0.9) WITHIN GROUP (ORDER BY …)
       COUNT(*)                                    AS orders
FROM meridian.orders
WHERE status = 'paid';

Always report the count next to any average or median: a median of 12 orders is a much weaker claim than a median of 12,000.

Ask your AI assistant

When an assistant gives you an average, ask: “What are the median and the 90th percentile, and how many records is this based on?” The free AI Answer Checker adds that question whenever an answer contains an average.

FAQ

When should I use the median instead of the average?

When the data is skewed or has outliers — money, time, counts per user — and you want to describe the typical case. Use the average when you need totals or unit economics, and report both when in doubt.

Why is the average higher than the median?

Because a minority of large values pulls the average up while the median only looks at the middle. On Meridian the average order is €60.92 and the median €43.96; the top 10% of orders bring 31.7% of the money.

Is average order value (AOV) a mean or a median?

By convention AOV is the mean: revenue divided by orders. That makes it useful for totals, and misleading as a description of a typical order. Report the median basket next to it. See AOV in the glossary.

Can I average the averages of several groups?

Only if you weight each group by its size. Otherwise small groups get as much influence as large ones. Group medians generally cannot recover the overall median; compute it from the underlying values.