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

Solution:

According to the given condition,

$\begin{array}{l} 6 .80 = \frac{[\begin{array}{c} (6 - a)^{2} + (6 - b)^{2} + (6 - 8)^{2} \\ + (6 - 5)^{2} + (6 - 10)^{2} \end{array}]}{5} \\ \Rightarrow 34 = (6 - a)^{2} + (6 - b)^{2} + 4 + 1 + 16 \\ \Rightarrow (6 - a)^{2} + (6 - b)^{2} = 13 = 9 + 4 \\ \Rightarrow (6 - a)^{2} + (6 - b)^{2} = 3^{2} + 2^{2} \\ \Rightarrow a = 3, b = 4 \end{array}$

Solution:

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