Statistics in everyday life

Statistics is the science of collecting, analysing and interpreting data. It underlies medical trials, opinion polls, economic reports, sports analysis and weather forecasts. News stories are full of numbers, and understanding a few basic ideas makes it much easier to tell solid evidence from misleading claims.

The mean is the total divided by the number of values. The median is the middle value when data are sorted. The mode is the most common value. Each can tell a different story.

Income is a classic example. A few very high earners pull the mean upward, so the median income is usually a better guide to what a typical person earns. When a report mentions an average, it is worth asking which average it means.

Averages alone hide how spread out data are. Two cities might have the same average temperature, but one could be mild all year and the other swing between hot summers and freezing winters.

The range and the standard deviation describe spread. A small standard deviation means values cluster near the mean; a large one means they vary widely. Many natural measurements, such as heights, roughly follow a bell-shaped normal distribution.

It is rarely possible to measure an entire population, so researchers study a sample. A good sample must be representative. In 1936 the Literary Digest magazine polled millions of people and predicted that Alf Landon would defeat Franklin Roosevelt. Roosevelt won in a landslide; the magazine's sample, drawn largely from telephone and car owners, was skewed toward wealthier voters.

Random sampling helps avoid such bias. Even good samples have some uncertainty, which is why polls report a margin of error. A small lead within the margin of error does not show that one side is truly ahead.

Two things moving together, a correlation, does not prove that one causes the other. Ice cream sales and drowning deaths both rise in summer, but ice cream does not cause drowning; hot weather affects both. A hidden factor like this is called a confounding variable.

Randomised controlled trials, which assign people randomly to receive a treatment or not, are the strongest way to test causes, because randomisation balances confounding factors between groups. This is why they are the standard for testing new medicines.

• Relative versus absolute risk: a risk that doubles from 1 in 10,000 to 2 in 10,000 is still very small.
• Truncated graph axes that exaggerate small differences.
• Cherry-picking time periods or data that support a particular conclusion.
• Small samples that produce dramatic but unreliable results.
• Survivorship bias: studying only successes, such as famous college dropouts, while ignoring the many who did not succeed.
• Percentages without the base number they refer to.