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

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

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

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

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

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

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

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

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

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

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

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?

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

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