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The mean of the numbers a, b,8,5 and 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?

a
a=3,b=4
b
a=0,b=7
c
a=5,b=2
d
a=1,b=6

detailed solution

Correct option is A

According to the given condition,                  6.80=(6−a)2+(6−b)2+(6−8)2+(6−5)2+(6−10)25⇒        34=(6−a)2+(6−b)2+4+1+16⇒        (6−a)2+(6−b)2=13=9+4⇒        (6−a)2+(6−b)2=32+22⇒        a=3,b=4

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