Unequal Averages
Play around with sets of five numbers and see what you can discover about different types of average...
Problem
Unequal Averages printable sheet
This problem follows on from M, M and M and About Average, so you may want to look at these first.
Here's an interesting set of five numbers: $$2, 5, 5, 6, 7$$ The mean, mode, median and range are all 5.
Can you find other sets of five positive whole numbers where:
Mean = Median = Mode = Range
Can you find sets of five positive whole numbers that satisfy the following properties?
A. Mode < Median < Mean
B. Mode < Mean < Median
C. Mean < Mode < Median
D. Mean < Median < Mode
E. Median < Mode < Mean
F. Median < Mean < Mode
Not all of these can be satisfied by sets of five numbers! Can you explain why?
Show that some of them can be satisfied with sets of just four numbers.
Show that all of them can be satisfied with sets of six numbers.
If you enjoyed this problem, you may be interested in Wipeout
Teachers' Resources
This problem featured in an NRICH webinar in December 2020.
You may wish to look at Wipeout as a follow-up activity.
The Inquiry Maths website offers a related activity and explains how it can be used as an inquiry prompt in the classroom.
Here is a photo of some of the contributions offered by delegates at the ATM Conference in 2015.
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