### Bat Wings

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

### Ice Cream Pie

The pie chart shows the different types of ice creams on sale. How many chocolate ice creams were sold?

### 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?

# Mean Balance

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

If  is less than 6, then adding another  to the set would make the mean smaller.

If  is more than 6, then adding another  to the set would make the mean larger.

But adding another  to the set does not change the mean, so  must be exactly 6.

Alternatively:

If the mean of the seven numbers is 6, they must add up to 42.
If the mean of eight numbers is 6, they must add up to 48.
Therefore the eighth number is 48 - 42 = 6

So the mean of the set of numbers 8, 4, 5, 4, , 6, 6 is 6.

That means that ( 8 + 4 + 5 + 4 +  + 6 + 6 ) $\div$ 7 = 6,
so 8 + 4 + 5 + 4 +  + 6 + 6 = 42,
so 33 +  = 42, so  = 9.

So  = 9 and  = 6.

You can find more short problems, arranged by curriculum topic, in our short problems collection.