Tukuk-OSThree different “averages” answer different questions. The mean is the total divided by the count — the maths of sums and budgets. The median is the middle value once everyone is sorted — the person with exactly as many people above as below. The mode is the most common. With a tidy symmetric group they nearly coincide; with any long tail they split violently. Put four salaries of 30,000 and one of 1,000,000 in a room: the mean is 214,000 — true, and useless. The median is 30,000, and it is why statisticians insist on median income, median house price, median sleep: the middle survives billionaires.
The mean only lies when you use it to describe “a typical member”; its real job is totals. “Average family has 2.4 children” sounds odd but predicts school enrolments perfectly, because average × families = children. Misuse arrives with per-capita statistics: “average sugar consumption per person: 40 kg/year” hides that some people drink none and others two soft drinks a day — an average is a distribution flattened into a number, and the interesting truth lives in the shape, not the flattening.
Two habits immunise you: whenever you see “average”, ask “mean or median?”; whenever you see a difference between averages, ask about spread. Two towns with average temperature 20 °C can differ — one steady 19–21, one swinging 5–35 — and only the second needs a heavy coat. Always ask how many (a “58% satisfaction” from 12 respondents is noise wearing a percentage).