Summarising without fooling yourself

The second stop in this reading is point 3 of the agent's report:

The average ticket remains stable (€7.40 versus €7.45), so the drop does not come from customers spending less on each visit.

There are two different sentences here. The first is a summary: one number per year. The second is a conclusion about hundreds of thousands of visits, drawn from the fact that two averages are similar. A well-chosen summary supports a conclusion like that; a badly chosen one manufactures it. To know which is the case you need to understand what an average measures, what it does not measure and which other numbers were at hand.

By the end you will be able to choose between mean and median according to the shape of the data, accompany the centre with a measure of dispersion and carry out three checks before trusting a summary you are handed.

@LLA - Media, mediana y dispersión: un conjunto de datos en dos números

Before reading the next lesson, do the practice. You will see four tables with the same statistics: bet on whether they are the same and only then look at them plotted. Then drag a point and watch how much the mean, the correlation and the line move because of a single data point.

@DDA - Práctica: El cuarteto de Anscombe

@AVI - El cuarteto de Anscombe: mira los datos antes de fiarte del resumen

Takeaways

• A summary is two numbers, centre and dispersion, and you have to say which ones have been chosen.
• The mean lets itself be dragged by the extremes and the median does not: with amounts, always ask for both.
• Two identical summaries do not guarantee identical data: plot, sort and look at the extremes.
• In the report: the average ticket holds up because it is propped up by thirty corporate orders, 0.3% of the tickets in the sample and 16.5% of its sales. The median falls from €4.94 to €4.57 and, without those orders, the average goes from €6.50 to €6.20. The over-the-counter customer does spend less on each visit.