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Range of Averages

Age 11 to 14 Short
Challenge Level

12 is the mode, so 12 must appear at least twice.

The median, 14, is half way between the two middle numbers when listed in order of size. So the 12s must be below the median, since the median is greater than 12.

12, 12     ,      

14 is half way between 12 and 16, so the next number is 16.

12, 12, 16     

The last number must be 22, so that the range is 10.

12, 12, 16, 22

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