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Choose the Mean

Age 11 to 14 Short Challenge Level:

 
For the mode to be 9, at least two of the numbers must be 9s.

The median and the mean are both smaller than 9, so the other numbers must be smaller than 9.

_ _ 9 9

The median will be halfway between 9 and the next largest number, so if the median is 8, then the next largest number must be 7.

_ 7 9 9

Then 9, 9, 7 and the fourth number must have a mean of 7, so, since there are 4 of them, they must have a total of 7$\times$4 = 28.

So the numbers are:

3 7 9 9



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