# Statistics - June 2006, All Stages

## Problems

### Domino Sorting

##### Stage: 1 Challenge Level:

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

### Name the Children

##### Stage: 1 Challenge Level:

Can you find out in which order the children are standing in this line?

### Compare the Squares

##### Stage: 2 Challenge Level:

In this problem you will do your own poll to find out whether your friends think two squares on a board are the same colour or not.

### Match the Matches

##### Stage: 2 Challenge Level:

Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.

### Presenting the Project

##### Stage: 2 Challenge Level:

Have a look at all the information Class 5 have collected about themselves. Can you find out whose birthday it is today?

### Real Statistics

##### Stage: 2 Challenge Level:

Have a look at this table of how children travel to school. How does it compare with children in your class?

### Substitution Cipher

##### Stage: 3 Challenge Level:

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

### 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 and generate a sequence where the next number is the mean of the last two numbers...

### 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.

### PDF

##### Stage: 5 Challenge Level:

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

### Maximum Scattering

##### Stage: 5 Challenge Level:

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

### Over-booking

##### Stage: 5 Challenge Level:

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?