Level 5: Spread and samples

Statistics and data · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you chose a fair average and drew data honestly. In this level you look past the middle: you cut data into quarters, draw the famous box plot, and use a simple rule to decide which values are truly unusual. Then the level turns to the biggest question in statistics: how can a sample of a few hundred people tell us about millions, and how does a sample go wrong? You learn the main ways to choose a sample, and the kinds of bias that have fooled even famous polls.

Lesson	You will be able to
Quartiles and the five-number summary	Find the minimum, Q1, median, Q3 and maximum of any list, and explain why calculators can disagree slightly
Box plots	Draw a box plot from a five-number summary, read percents from it, and compare two groups side by side
Interquartile range and outliers	Measure the spread of the middle half with the IQR, and use the 1.5 × IQR rule to find outliers
Populations and samples	Tell a population from a sample and a census from a survey, and estimate a whole from a part
Sampling methods	Choose a simple random, systematic, stratified or cluster sample, and explain why convenience and voluntary samples are unfair
Bias	Name sampling, non-response, response and measurement bias, and explain how the 1936 Literary Digest poll went wrong

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