1. A list of numbers has an average of 51. A new list is formed by subtracting 50 from every number on the original list. The r.m.s. of the numbers on the new list is 3.0.
(a) Find the average of the new list.
(b) Find the SD of the original list.
2. A list of numbers has an r.m.s. of 4.0. A new list is formed by adding 3 to every number on the list. The new list has an r.m.s. of 5.0.
(a) Find the average of the original list.
(b) Find the SD of the original list.
3. A list of numbers has an average of 40 and an SD of 15. A new list is formed by adding 10 to every number on the list. If possible, find the r.m.s. of the numbers on the new list. If it is not possible, explain why not.