Mean vs median vs mode: which average should you use?

One number can gaslight a whole report. Mean, median and mode answer three different questions, and dashboards quietly pick the wrong one all the time. Here is the whole thing on one page. The print-ready A4 PDF is at the bottom.

The three

• Mean: sum / count. Every value counts, which is the feature AND the bug.
• Median: the middle value once sorted.
• Mode: the most frequent value.

When each lies

• Mean + one outlier: one CEO salary skews the whole team's number.
• Median + tiny samples: jumpy under about 30 rows.
• Mode + continuous decimals: every value is unique, so there is no "most frequent".

In SQL

SELECT
  AVG(salary)              AS mean_salary,   -- 72,400
  PERCENTILE_CONT(0.5)
    WITHIN GROUP (ORDER BY salary)
                           AS median_salary  -- 48,000
FROM team;

Both numbers are correct. Only one describes a person who exists. For the mode: GROUP BY salary ORDER BY COUNT(*) DESC LIMIT 1.

In pandas

• s.mean(): the mean.
• s.median(): the median.
• s.mode()[0]: the mode, first one if tied.

Pick one

• Salaries, prices, delays: median.
• Categories, shoe sizes: mode.
• Symmetric data with no outliers: the mean is fine, and it sums back to totals.

The trap table

Cheap tell in one second: mean far above median means right skew, a few big values dragging it up. Look at the distribution before you report either.