# Statistics - June 2006, Stage 3&4

## Problems

### Archery

##### Stage: 3 Challenge Level:

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

### Top Coach

##### Stage: 3 Challenge Level:

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

### Litov's Mean Value Theorem

##### Stage: 3 Challenge Level:

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

### Substitution Cipher

##### Stage: 3 and 4 Challenge Level:

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

### The Mean Problem

##### Stage: 4 Challenge Level:

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. . . .

### The Rescaled Map

##### Stage: 4 Challenge Level:

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.