The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, find the values of a and b?

Solution :

According to given condition,

6.80 = \((6-a)^2 + (6-b)^2 + (6-8)^2 + (6-5)^2 + (6-10)^2\over 5\)

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

\(\implies\)  \((6-a)^2 + (6-b)^2\) = 13

\(\implies\)  \((6-a)^2 + (6-b)^2\) = 13 = \(3^2\) + \(2^2\)

\(\implies\)  a = 3 and b = 4

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