Katherine earned 84, 92, 84, 75, and 70 on her five math tests.

What is the minimum grade Katherine needs to earn on the next test to have a mean of 84?

Katherine's marks = 84,92,84,75,70

Total marks = 84+92+84+75+70 = 405

No. of observations = 5

Mean = Total sum of observations/No. of observations

Mean = 405/5=81

Expected mean = 84

Let expected total marks be = n

84=n/5

84*5=n

n=420