In these activities, you can be playful with averages, looking for patterns in the way the mean, median and mode change when you vary the numbers in a set.
Why the humble average can be grossly misleading.
We are used to calculating the mean, median and mode from a set of numbers, but can you find the numbers if you know the averages?
Imagine you have a large supply of 3kg and 8kg weights. This problem invites you to explore the means of different sets of these weights.
Can you find sets of numbers whose mode, mean, median and range are all the same?
Can you find sets of numbers where mean < median < mode? Or median < mean < mode? Or...
Take a set of numbers and wipe one of them out. How does the average change? Can you do a little mathematical detective work to figure out which one? Can you develop a strategy?