Statistics - June 2006, Stage 4&5

Problems

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Substitution Cipher

Stage: 3 and 4 Challenge Level: Challenge Level:1

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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The Mean Problem

Stage: 4 Challenge Level: Challenge Level:1

There are four unknown numbers. The mean of the first two numbers is 4, and the mean of the first three numbers is 9. The mean of all four numbers is 15. If one of the four numbers was 2, what were. . . .

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The Rescaled Map

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

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PDF

Stage: 5 Challenge Level: Challenge Level:1

Given a probability density function find the mean, median and mode of the distribution.

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Maximum Scattering

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

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Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?