# 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?

### The Mean Problem

##### Stage: 3 Short Challenge Level:

Can you work out the four unknown numbers from the clues about their means?

### 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 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?