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Things to know about maths: Difference between revisions
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Amwelladmin (talk | contribs) (Created page with "{{a|devil|}}The JC was never very good at maths — still isn’t — yet found himself, to his own great surprise, conducting a long if unspectacular career in financial services. At last count, 30 years. Along the way he has learned some helpful, if unintuitive, things, so it seems only right to collect them. ==Averages are misleading== ===Ergodicity=== “Ensemble averages” payoffs across a collection of people who roll the same dice once, are very different from t...") |
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“Ensemble averages” payoffs across a collection of people who roll the same dice once, are very different from the payoffs of the same person rolling the same dice repeatedly. This is why the house never loses. This is called ''[[ergodicity]]''. | “Ensemble averages” payoffs across a collection of people who roll the same dice once, are very different from the payoffs of the same person rolling the same dice repeatedly. This is why the house never loses. This is called ''[[ergodicity]]''. | ||
===Non-representative=== | ===Non-representative=== | ||
The average of a collection of measurements taken from real people, in itself, represents absolutely nothing. Taking new measurements which change the average does not affect any of the existing measurements. Call this the “[[ | The average of a collection of measurements taken from real people, in itself, represents absolutely nothing. Taking new measurements which change the average does not affect any of the existing measurements. Call this the “[[Techbro on the Clapham Omnibus]]” problem, known in modern times as the “making a big hire to massage the [[diversity and inclusion]] stats” problem. | ||
===Grouping data is [[problematic]]=== | ===Grouping data is [[problematic]]=== | ||
An average or trend which seems to point in one direction can, when you group the data differently, often point in another direction. This plays particular havoc with social scientists when they try to draw causal inferences — or moral imperatives — from data they have gathered with the careful intention of illustrating their own precious hypothesis. | An average or trend which seems to point in one direction can, when you group the data differently, often point in another direction. This plays particular havoc with social scientists when they try to draw causal inferences — or moral imperatives — from data they have gathered with the careful intention of illustrating their own precious hypothesis. | ||