In Module 0 you saw that competitor prices are a cloud, not a point. Now we learn to describe that cloud precisely — picture it, find its centre, measure its spread, locate any value inside it — and turn the description into an actual answer to "what should we charge?"
You walked Geneva and recorded the price of a Margherita at 30 pizzerias. Those 30 are a sample from the population of all Geneva pizzerias. Any number you compute from the 30 — the average, say — is a statistic; the unknown true value across all pizzerias would be a parameter. This distinction runs through the whole course.
Knowing a variable's type decides which display and which statistic are even legal. Tap each card to flip it.
Before any average, plot the data. A histogram groups prices into bins and shows how many fall in each. Drag the bin width and watch the story change — too wide hides detail, too narrow turns it into noise.
The tail stretches to the right — a few pricey tourist spots. That is a right-skewed distribution, and it will matter the moment we pick an average.
A histogram shows shape but loses the actual values. A stem-and-leaf plot shows the shape and every price: the stem is the tens digit, each leaf is a ones digit.
Read it sideways: it is a histogram you can still read the raw data off.
For symmetric data they roughly agree. For skewed data they split — and the gap is the lesson.
The mean chases extremes; the median resists them. Report the median when a few big values would otherwise mislead.
Below, Pâquis and Rive both average CHF 18. But one is tightly clustered and one is all over the map. The standard deviation (the typical distance from the mean, from Module 0) and the interquartile range put a number on that difference.
Three rulers for spread, weakest to strongest: range (max − min, fooled by one outlier), IQR (the middle 50%, resistant), and standard deviation (uses every value).
Sort the data and you get five landmarks: minimum, Q₁, median, Q₃, maximum. The box plot draws them: a box from Q₁ to Q₃ (the middle 50%), a line at the median, whiskers to the data, and dots for outliers.
A z-score says how many standard deviations a value sits from the mean: z = (x − mean) ÷ s. Type a competitor's price and see.
A z near 0 is typical; |z| above ~2 is genuinely unusual. z-scores let you compare positions across different datasets on one ruler.
Suppose your pizzeria's daily covers (customers served) are bell-shaped with mean 120 and standard deviation 15. The Empirical Rule says ≈68% of days fall within ±1 SD, ≈95% within ±2, ≈99.7% within ±3. Slide to see the band.
Chebyshev makes no shape assumption: at least (1 − 1/k²) of any data lies within k standard deviations. Weaker than 68–95–99.7, but always true. Compare the two columns above as you slide.
The Empirical Rule is a generous estimate that needs a bell; Chebyshev is a cautious guarantee that needs nothing.
The competitor data, described: a typical price (the median), a middle-of-the-market band (Q₁ to Q₃, where half of all pizzerias sit), and a clear outlier you should ignore. Pick your Margherita price and see exactly where it lands among the competition.
"Around the median, inside the middle 50%" is a position you can justify to your partner and your bank. That is the whole job of descriptive statistics: turning a cloud into a defensible decision.