Statistics at Alevel: What its all about

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Statistics at A-levelWhat its all about
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Probability versus Statistics

• Probability Know the true situation, predict the
  outcome of events
• If I roll a die 5 times, what is the probability
  of getting 3 sixes?
• What is the average number of sixes Ill get?
• Statistics Sample data to make predictions about
  the whole population and to test hypotheses

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Probability

• Discrete distributions
• If I roll a die 12 times, what is the
  probability of getting 0, 1, 2, 3, sixes?
  (Binomial)
• And what is the probability that it will take 1,
  2, 3, 4, rolls before my first six?
  (Geometric)
• If there are an average of three buses an hour,
  what is the probability of 0, 1, 2, 3, 4, buses
  arriving during this hour? (Poisson)
• What are the means and variances of the answers
  (distributions)?

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Probability

• Continuous distributions
• What is the probability that a randomly chosen
  girl from Year 10 will be taller than 1.65m
  (given the mean and standard deviation of Year 10
  girls heights)? (Normal)
• Given that a lightbulb has a mean lifetime of
  300 hours of use, what is the probability that a
  lightbulb lasts more than 350 hours?
  (Exponential)

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Statistics

• Estimating population statistics
• A sample of 50 bars of chocolate, each
  supposedly weighing 100g, had a mean mass of
  99.7g and standard deviation of 0.6g. What can
  be said about the mean mass of this brand of
  chocolate bar?
• In a recent survey, 107 people were asked
  whether they supported the latest Government Bill
  on XYZ, and 68 said yes. What can be said about
  the percentage of the population supporting this
  Bill?

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Statistics

• Hypothesis testing
• Year 11 boys are taller than Year 11 girls
• Year 10 girls have a higher average IQ than Year
  10 boys
• but they also have a higher standard deviation
  in their IQ
• A greater proportion of girls walk to school
  than boys

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Statistics

• Correlation
• Hypothesis testing The higher the IQ of the
  student, the better their KS2 SATs results
• Estimating population statistics Find a best
  fit (regression) line for the IQ/KS2 SATs data