Reading Numbers in the News

News stories, adverts and social posts are full of averages, polls and huge numbers. A few questions help you see what a number really means. (Relative versus absolute risk and misleading charts are covered in Critical Thinking: Statistics and Charts in the News; this lesson adds averages, polls and scale.)

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Three kinds of average

• La Trobe University's maths guide defines the mean as the total divided by the number of values, the median as the middle value, and the mode as the most common value.
• La Trobe's example: for the scores 10, 5, 9, 8, 6, 5, 9, 8, 7, 6, 5, 6, the mean is 84 / 12 = 7, and the median is 6.5 (the two middle values, 6 and 7, averaged).
• La Trobe notes that the mean is sensitive to outliers (unusually large or small values), and that the median is preferred when there are extreme scores.
• Worked example: nine people earn AED 10,000 a month and one earns AED 200,000. The mean is AED 29,000, but the median is AED 10,000. Which one describes a 'typical' person better?
• This is why official statistics often use the median for income: the UK Office for National Statistics reported median household disposable income of 34,500 pounds for the financial year ending 2023.

Polls and samples

• Most surveys ask a sample, not everyone. The result carries a margin of error.
• Pew Research Center, for a survey of 1,501 adults, stated with 95 percent confidence that sampling error was plus or minus 3 percentage points.
• Smaller groups have bigger margins: in the same Pew survey, subgroups of around 470 to 570 people had margins of plus or minus 5 points.
• Worked example: if a poll shows 48 percent against 45 percent with a margin of plus or minus 3 points, the true figures could overlap, so the 'lead' may not be real.
• Pew also notes that question wording and practical difficulties can add error beyond the sampling margin.

The Royal Statistical Society's checklist

• The Royal Statistical Society's Getstats campaign proposed rules of thumb for journalists, reported by journalism.co.uk in 2012. They are just as useful for readers.
• Check the source: who produced the figure, and do they have something to sell?
• Check the sample (does it represent the wider group?) and check the question (what did people actually answer?).
• Check the average: which type is being used?
• Do not over-read one change: a single movement is not a trend. And give a base: frequencies are clearer as, for example, 'per 1,000 people'.

Getting a feel for big numbers

• Millions and billions sound similar but are very different: a million seconds is about 11.6 days; a billion seconds is about 31.7 years.
• To compare places of different sizes, convert totals to rates, such as per 1,000 people (the RSS 'give a base' rule).
• Divide a big national figure by the population to get a per-person amount you can picture.
• Ask 'is that a lot?' and look for a comparison: last year, another country, or the total budget.