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### Number and algebra

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### For younger learners

# Very Old Man

Li Ching-Yuen himself gave a hint as to the secret of long life. It was

* Keep a quiet heart * Sit like a tortoise * Walk sprightly like a pigeon * Sleep like a dog

If this hint is not enough to help, try plotting the data on a chart. If there is a 50% chance, say, of death each year, by what factor might the expected numbers of living very old people reduce over 5 years? Can you find a percentage which might fit the data?

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### Chi-squared Faker

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Age 16 to 18

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Li Ching-Yuen himself gave a hint as to the secret of long life. It was

* Keep a quiet heart * Sit like a tortoise * Walk sprightly like a pigeon * Sleep like a dog

If this hint is not enough to help, try plotting the data on a chart. If there is a 50% chance, say, of death each year, by what factor might the expected numbers of living very old people reduce over 5 years? Can you find a percentage which might fit the data?

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?