Basic Statistics for Citizens

Mean vs Median: Why It Matters

The mean (average) adds all values and divides by the count. The median is the middle value when all values are ranked. For symmetrical distributions, they are similar. For skewed distributions — like income — they diverge dramatically.

In the US, the mean household income is roughly $105,000, but the median is about $75,000. The mean is pulled up by billionaires; the median better represents the typical household. When a politician says 'average income is rising,' check whether they mean the mean or median — it is possible for mean income to rise while most people get poorer, if gains are concentrated at the top.

Per Capita Figures and Percentages

Raw numbers without context are misleading. '1,000 new COVID cases' means something very different in a country of 5 million than in one of 1.4 billion. Per capita figures (dividing by population) allow meaningful comparison.

Percentages can also mislead. A '50% increase' in a rare disease that affected 2 people now affects 3 — hardly alarming. A '2% increase' in heart disease deaths could mean tens of thousands of additional deaths. Always look for the base number behind a percentage change.

Worked Example: When the Average Lies

Imagine a small firm with nine employees. Here are their annual salaries, in thousands of dollars:

The mean is the sum divided by the count: (30+32+34+36+38+40+42+44+460) = 756, and 756 / 9 = $84,000. The median is the middle value once the numbers are sorted — the fifth of nine — which is $38,000.

Eight of the nine employees earn below the mean. Reporting 'the average salary here is $84,000' is technically true yet deeply misleading, because one extreme value (the owner) drags the mean upward. The median, unaffected by that single outlier, describes the typical worker far better. As a rule of thumb: when a distribution is skewed — incomes, house prices, wealth, city sizes — prefer the median.

Per-Capita Turns Totals Into Comparisons

Totals reward size; per-capita figures enable fair comparison. Suppose Country A emits 500 million tonnes of CO2 and Country B emits 50 million tonnes. A looks like the bigger polluter. But if A has 300 million people and B has 5 million, then per person A emits 1.67 tonnes while B emits 10 tonnes — B is six times more carbon-intensive per resident. Whenever you compare places or groups of different sizes, ask whether the figure has been normalised (per capita, per $1,000 of GDP, per 100,000 people). An unnormalised total often smuggles in a hidden comparison of population rather than of the thing you actually care about.

Don't Forget the Spread

A centre without a spread is half a story. Two neighbourhoods can share a median income of $50,000 while one ranges from $45,000 to $55,000 and the other from $10,000 to $250,000. The standard deviation (or the interquartile range) captures that difference. A useful shortcut is the range and the shape: if the mean sits far above the median, the distribution is right-skewed with a long upper tail, and a single summary number will mislead. Whenever a report gives you only an average, ask for the spread and the shape before drawing conclusions — the same mean can describe wildly different realities.