Repost :
Median = 62kg. That's the middle boy of the 7 of them.
Mean = 61kg, so total mass of 7 boys = 61kg x 7 = 427kg
Mode = 68kg, so we know there is more than 1 boy who is 68kg. This also means at least 2 boys are 68kg.
Lightest boy is 50kg. So no one is lighter than 50kg.
Approach : Subtract the masses of the boys that are known first to get the remaining mass
427kg - 50kg - 62kg - 68kg - 68kg = 179kg
So 179kg is the mass of the remaining 3 boys. And the heaviest boy should be one of them.
We want the highest possible mass of the heaviest boy. So we should make the other 2 boys as light as possible.
We can let them be 51kg and 52kg.
Therefore, highest possible mass of heaviest boy = 179kg - 51kg - 52kg = 76kg
The masses (in kg) are :
50 51 52 62 68 68 76