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In order to calculate the mean height, Snow White had to first calculate the sum of the heights of the Dwarves.

She calculated their mean height as 112.3 cm, so their heights must have added up to 

7 $\times$ 112.3 = 786.1

Since Doc is 3.5 cm taller than Dopey, their heights really add up to

786.1 $+$ 3.5 = 789.6

Therefore the mean height of the Seven Dwarfs is

789.6 $\div$ 7 = 112.8



This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.