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

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

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

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

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

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

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?

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

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