Mean, Median, Mode
Six salaries, `[52, 55, 58, 60, 64, 240]`, and two honest people report the typical pay as $88k and $59k. Both did the arithmetic right; the number you trust depends on which question you asked.
- ▸Two honest people compute the 'typical' salary on one team and hand you numbers $29k apart, both correct.
- ▸One giant value hijacks the average and leaves the middle untouched, and the distance between them measures the lean.
- ▸Picking how to average was secretly picking a cost to minimize, the same choice machine learning makes.
Take those six salaries and ask for a single number that stands in for the whole team. There are three honest ways to get one, and they start from three different rules.
Add every salary and split the total evenly, so everyone gets the same share. That share is the balance point of the data: nudge any salary up and the share slides up with it.
Now line the salaries up smallest to largest and point at the middle of the row. Half the team earns less, half earns more. Only a salary's *position* in line matters here, not how large the top number climbs.
Or count how often each value shows up and keep the one that appears most. On six all-different salaries that barely helps, but ask 'what is the most common pay band' and it is the only rule that answers.
On a tidy, symmetric team all three rules land on the same number, so they look interchangeable. The whole topic is about what pulls them apart.