### Bat Wings

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

### Kate's Date

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

### Balancing the Books

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

# Unequal Averages

##### Age 11 to 14 Challenge Level:

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:

Mean = Median = Mode = Range

Can you find sets of five positive whole numbers that satisfy the following properties?

Mode < Median < Mean

Mode < Mean < Median

Mean < Mode < Median

Mean < Median < Mode

Median < Mode < Mean

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.

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