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Jean Claude Girard Universit Claude Bernard Lyon-1 Institut de Formation des Ma tres de l Acad mie de Lyon, France

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Jean Claude Girard Universit Claude Bernard Lyon-1 Institut de Formation des Ma tres de l Acad mie de Lyon, France

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    2. Descriptive statistics at the « College » level (grade 6 to 9) : bar chart, pie chart, scatter plot, histogram mean, median, mode, range No randomness nor probability before grade 10 (until now, changes expected next year)? At the « lycée » level Grade 10 : Simulation, sampling fluctuation Grade 11 : Quartile, decile. Box-plot . Variance, standard deviation. Discrete Probability distribution modeling a random experiment. Frequentist approach of the probability. Grade 12 : Binomial distribution, goodness-of-fit test (for n equally likely events). Descriptive statistics at the « College » level (grade 6 to 9) : bar chart, pie chart, scatter plot, histogram mean, median, mode, range No randomness nor probability before grade 10 (until now, changes expected next year)? At the « lycée » level Grade 10 : Simulation, sampling fluctuation Grade 11 : Quartile, decile. Box-plot . Variance, standard deviation. Discrete Probability distribution modeling a random experiment. Frequentist approach of the probability. Grade 12 : Binomial distribution, goodness-of-fit test (for n equally likely events).

    6. 1st example (from the guideline of the french curriculum)? We throw a die. When tossing a 6, the rabbit finishes. When tossing 1,2,3,4 or 5 the turtle moves from a case to the next one. The first to finish is the winner. Who (the rabbit or the turtle) is the more likely to win ?1st example (from the guideline of the french curriculum)? We throw a die. When tossing a 6, the rabbit finishes. When tossing 1,2,3,4 or 5 the turtle moves from a case to the next one. The first to finish is the winner. Who (the rabbit or the turtle) is the more likely to win ?

    8. Jean de La Fontaine (1621 – 1695)?Jean de La Fontaine (1621 – 1695)?

    9. 1st example We throw a die. When tossing a 6, the rabbit finishes. When tossing 1,2,3,4 or 5 the turtle moves from a case to the next one. The first to finish is the winner. Who (the rabbit or the turtle) is the more likely to win ?1st example We throw a die. When tossing a 6, the rabbit finishes. When tossing 1,2,3,4 or 5 the turtle moves from a case to the next one. The first to finish is the winner. Who (the rabbit or the turtle) is the more likely to win ?

    10. The results The hare is the winner with a relative frequency between 0,55 and 0,74. The median and the mean are about 0, 665 that is to say appromatively the theoretical probability 1 –(5/6)^6 80 per cent of the results are in the interval [0,61 ; 0,711 ] less than 0,05 from this probability. We can observe sampling fluctuations but we can’t have wathever result.The results The hare is the winner with a relative frequency between 0,55 and 0,74. The median and the mean are about 0, 665 that is to say appromatively the theoretical probability 1 –(5/6)^6 80 per cent of the results are in the interval [0,61 ; 0,711 ] less than 0,05 from this probability. We can observe sampling fluctuations but we can’t have wathever result.

    11. Cumulating the results of the repeated games, the « limit » of the relative frequency of the cases in which the hare is the winner is the probability 0,665. Cumulating the results of the repeated games, the « limit » of the relative frequency of the cases in which the hare is the winner is the probability 0,665.

    13. Second example (from Hyperbole, Math Terminale ES, Nathan, 2002)?Second example (from Hyperbole, Math Terminale ES, Nathan, 2002)?

    14. This table sum up the results when throwing a dice one thousand times. Is this dice fair ?This table sum up the results when throwing a dice one thousand times. Is this dice fair ?

    15. This multiple bar-chart (observed Relative Frequency vs Probability) does not allow us to come to a conclusion.This multiple bar-chart (observed Relative Frequency vs Probability) does not allow us to come to a conclusion.

    16. Au cas où le lien ne fonctionnerait pas D^2 = ?(fi – pi)^2 1000 D^2 ˜ 1,603 Au cas où le lien ne fonctionnerait pas D^2 = ?(fi – pi)^2 1000 D^2 ˜ 1,603

    17. Au cas où le lien ne fonctionnerait pas Result of the simulation : D9 = 1,4846 We do not accept the hypothesis Au cas où le lien ne fonctionnerait pas Result of the simulation : D9 = 1,4846 We do not accept the hypothesis

    18.

    19. Third example from this book Introducing statistical inference, hypothesis test & p-value. Assuming an hypothesis, can random explain observed results ?Third example from this book Introducing statistical inference, hypothesis test & p-value. Assuming an hypothesis, can random explain observed results ?

    20. The« Castaneda v Partida » case, 1976. In Texas, a convicted mexican-american attacked the court because of the small number of mexican-american in the grand jury of this county during a past period of 11 years.The« Castaneda v Partida » case, 1976. In Texas, a convicted mexican-american attacked the court because of the small number of mexican-american in the grand jury of this county during a past period of 11 years.

    21. The Supreme Court commentary Modelling by a binomial distribution (in fact an hypergeometric distribution approximated by a binomial distribution)?The Supreme Court commentary Modelling by a binomial distribution (in fact an hypergeometric distribution approximated by a binomial distribution)?

    22. A random experiment suggested by the book « Prove it with figures » to simulate the situation. A random experiment suggested by the book « Prove it with figures » to simulate the situation.

    23. A dice with a probability of 0,791 for « head » is not easy to get, so we will use a urn model. Simulations from this model We never observe a result equal or less than 339. A dice with a probability of 0,791 for « head » is not easy to get, so we will use a urn model. Simulations from this model We never observe a result equal or less than 339.

    24. Au cas où le lien ne fonctionnerait pasAu cas où le lien ne fonctionnerait pas

    26. The end of the Supreme Court commentary : a calculation. The sampling variation can’t explain so small a number of mexican-american in the grand jury according to the hypothesis the choice is the result of a random drawing. The p-value is near 1/10^140 that’s to say approximately 0. To sum up, Random can’t explain everything. Notice : This does not prove discrimination. It would be interesting to ask the students why ?The end of the Supreme Court commentary : a calculation. The sampling variation can’t explain so small a number of mexican-american in the grand jury according to the hypothesis the choice is the result of a random drawing. The p-value is near 1/10^140 that’s to say approximately 0. To sum up, Random can’t explain everything. Notice : This does not prove discrimination. It would be interesting to ask the students why ?

    27. Toupie de Monterrey ! Whirligig ( or top ?) from MonterreyToupie de Monterrey ! Whirligig ( or top ?) from Monterrey

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