SOLUTION: If the mean and standard deviation of the following data are 5 and 2.1082 respectively, find A and B. 8 , 4 , A , B , 6 , 3 , 3 , 5 , 4.

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Question 1109222: If the mean and standard deviation of the following data are
5 and 2.1082 respectively, find A and B.
8 , 4 , A , B , 6 , 3 , 3 , 5 , 4.


Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
xbar=mean=%288+%2B+4+%2B+A+%2B+B+%2B+6+%2B+3+%2B+3+%2B+5+%2B+4%29%2F9=5

%2833+%2B+A+%2B+B%29%2F9=5

33+%2B+A+%2B+B=45

A%2BB=12

We use the shortcut formula for the variance:

s%5E2=%28sum%28x%5E2%29-n%2A%28xbar%29%5E2%29%2F%28n-1%29



s%5E2=%28A%5E2%2BB%5E2%2B175-9%2A%285%29%5E2%29%2F%289-1%29

s%5E2=%28A%5E2%2BB%5E2%2B175-9%2A25%29%2F8

s%5E2=%28A%5E2%2BB%5E2%2B175-225%29%2F8

s%5E2=%28A%5E2%2BB%5E2-50%29%2F8

s%5E2=%28A%5E2%2BB%5E2-50%29%2F8

2.1082%5E2=%28A%5E2%2BB%5E2-50%29%2F8

8%2A2.1082%5E2=A%5E2%2BB%5E2-50

35.55605792=A%5E2%2BB%5E2-50

85.55605792=A%5E2%2BB%5E2

A%5E2%2BB%5E2=85.55605792

We solve the system:

system%28A%2BB=12%2CA%5E2%2BB%5E2=85.55605792%29

by substitution and get these two solutions:

A=3.39654, B=8.60346
A=8.60346, B=3.39654

However that's just one solution since it doesn't matter 
which is A and which is B.

Edwin