Frequency constraints

A canteen records the capacities of drink cartons bought by its customers. Capacities 200, 250, 300, 350 and 400 mL have respective frequencies \(10,18,8,x,6\). Conditions in parts (a), (b) and (c) are independent.

1. If the unique mode is 250 mL, state the complete inequality satisfied by the integer frequency \(x\).[1]
2. If the median capacity is 300 mL, find the greatest possible value of \(x\).[3]
3. If x=7, calculate the mean capacity, correct to 1 decimal place.[2]
4. Which average should a canteen manager use to decide which capacity to order in the largest quantity? Explain.[1]