Removing and adding values

Core stretch

The list is \(1,6,10,14,19\).

1. Remove one value so that both the median and range are unchanged.[1]
2. A value \(p\) is instead added to the original list so its mean rises by 3. Find \(p\).[2]
3. A value \(q\) is added to the original list so its median decreases by 2. Find the greatest integer \(q\).[2]