Statistics: apply statistics to describe a population

The idea

Describing a population means turning a data set into a few figures and then saying what those figures mean about the group. Choose an average that suits the data: the mode for categories such as favourite sport, the median where a few very large or very small values would distort things, and the mean where you want every value to count. Pair the average with a measure of spread, because two groups can share a mean and still look nothing alike. For wages of £18000, £19000, £20000, £21000 and £90000 the mean is £33600, yet four of the five people earn less than that, so the median of £20000 describes a typical wage better. Questions give you a table or a chart and ask what it shows about the group, or ask which average is the fairest to use and why.

What earns the marks

• Naming the average or measure of spread chosen, with a reason that refers to the data such as an extreme value.
• Working that statistic out correctly, even if the conclusion drawn from it is then wrong.
• A statement about the group of people or items, not only about the numbers.
• Supporting that statement with a figure quoted from the table or diagram.

Common mistakes and how to put them right

• Quoting a mean and a range with no sentence saying what they show about the group.

• Using the mean on data holding one very large value and then calling it the typical amount.

• Describing the sample that was measured and calling the description true of the whole population.

• Giving a modal category as its frequency instead of naming the category itself.

Exam tips

• Answer in a full sentence that names the group and the quantity, for example "most club members finished in under 30 minutes".
• If asked which average to use, say what the other averages would get wrong on this particular data.
• Keep the units on every figure you quote, and round money to the nearest penny.