# Statistics - Stage 3

### Bat Wings

##### Age 11 to 14 Short Challenge Level:

Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?

### Litov's Mean Value Theorem

##### Age 11 to 14 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

##### Age 11 to 14 Short Challenge Level:

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

### Substitution Cipher

##### Age 11 to 14 Challenge Level:

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

### Reaction Timer

##### Age 11 to 14 Challenge Level:

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

### M, M and M

##### Age 11 to 14 Challenge Level:

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

### Searching for Mean(ing)

##### Age 11 to 14 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

### How Would You Score It?

##### Age 11 to 14 Challenge Level:

Invent a scoring system for a 'guess the weight' competition.

### Who's the Best?

##### Age 11 to 14 Challenge Level:

Which countries have the most naturally athletic populations?

### Olympic Records

##### Age 11 to 14 Challenge Level:

Can you deduce which Olympic athletics events are represented by the graphs?

### Statistical Shorts

##### Age 11 to 16 Challenge Level:

Can you decide whether these short statistical statements are always, sometimes or never true?

### Statistics Stage 3 - Short Problems

##### Age 11 to 14

A collection of short Stage 3 problems on statistics.

### Picturing the World

##### Age 11 to 14 Challenge Level:

How can we make sense of national and global statistics involving very large numbers?

### What's the Weather Like?

##### Age 11 to 14 Challenge Level:

With access to weather station data, what interesting questions can you investigate?

### Estimating Time

##### Age 11 to 14 Challenge Level:

How well can you estimate 10 seconds? Investigate with our timing tool.

##### Age 11 to 14 Challenge Level:

Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

### Wipeout

##### Age 11 to 14 Challenge Level:

Can you do a little mathematical detective work to figure out which number has been wiped out?

### Half a Minute

##### Age 11 to 14 Challenge Level:

Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?

### Unequal Averages

##### Age 11 to 14 Challenge Level:

Play around with sets of five numbers and see what you can discover about different types of average...

### Acceptance Rate

##### Age 11 to 14 Short Challenge Level:

The mean number of students has changed, so how many students applied to a school?

### Mean Median

##### Age 11 to 14 Short Challenge Level:

Can you work out the median weight of these children from the given means?

### Mean Balance

##### Age 11 to 14 Short Challenge Level:

Given information about the mean, can you work out the missing numbers?

### Mean Square

##### Age 11 to 14 Short Challenge Level:

Can you fill this square so that the number in the middle of each line is the mean of the two numbers on either side of it?

### A Mean Calculation

##### Age 11 to 14 Short Challenge Level:

What is the mean of this set of numbers?

### Committees

##### Age 11 to 14 Short Challenge Level:

Every member of the club is a member of two committees. How many members are there in the club?

### Choose the Mean

##### Age 11 to 14 Short Challenge Level:

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

### Average Temperature

##### Age 11 to 14 Short Challenge Level:

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

### Shifting Average

##### Age 11 to 14 Short Challenge Level:

What happens to the average if you subtract 8 from all of the numbers?

### French Test

##### Age 11 to 14 Short Challenge Level:

What was the average score in this French test?

### Number of Arms

##### Age 11 to 14 Short Challenge Level:

What is the probability that the next person you meet has an above average number of arms?

### Range of Averages

##### Age 11 to 14 Short Challenge Level:

Find these 4 numbers, given their mode, median and range.

### The Average Age

##### Age 11 to 14 Short Challenge Level:

Given this information about averages, find the ages of these teachers.

### Maximum Mean

##### Age 14 to 16 Short Challenge Level:

What is the largest that the mean of these numbers could be?