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### Number and algebra

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### Working mathematically

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### Advanced mathematics

# Unequal Averages

**Mean = Median = Mode = Range **

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*

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*Unequal Averages printable sheet*

*This problem follows on from M, M and M so you may want to look at that 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:**

**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.

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

When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?

How many visitors does a tourist attraction need next week in order to break even?