$\begin {array} {1 1} (A)\;a=0\: b=7 & \quad (B)\;a=5\: b=2 \\ (C)\;a=1\: b=6 & \quad (D)\;a=3\: b=4 \end {array}$

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According to the given condition

$ 6.80 = \large\frac{(6-a)^2+(6-b)^2+(6-8)^2+(6-5)^2+(6-10)^2}{5}$

$ \Rightarrow (6-a)^2+(6-b)^2+4+1+16=34$

$ (6-a)^2+(6-b)^2=34-21$

$ (6-a)^2+(6-b)^2=13$

$(6-a)^2+(6-b)^2=9+4$

$(6-a)^2+(6-b)^2=3^2+2^2$

$(6-a)^2 = 3^2 \: (6-b)^2 = 2^2$

$ 6-a = 3\: \: \:\: \: \: \: \:\; \: \: 6-b=2$

$ -a=-3\: \: \: \: \: \: \: \:\: \: \: \: -b=-4$

$ \: \: \: a = 3\: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: b=4$

Ans : (D)

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