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

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

Charlie has moved between countries and the average income of both has increased. How can this be so?

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?

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

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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

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

What do these statistics about family size mean?

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

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

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

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

Find the value of $m$ from these statements about a group of numbers

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

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

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

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

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

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

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?

Can you make all of these statements about averages true at the same time?

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

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

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

Kyle and his teacher disagree about his test score - who is right?

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