The mean of the numbers a, b, 8,5,10 is 6 and the variance is 6.80 , then which of the following gives possible values of a & b

Step-by-step solution

The mean of the numbers a, b, 8, 5, 10 is given by a + b + 8 + 5 + 10 5 = 6 . This simplifies to a + b + 23 = 30 , so a + b = 7 . The variance is given by ^2 = x_i^2 n - ( x )^2 = 6.8 . Substituting the values: a^2 + b^2 + 8^2 + 5^2 + 10^2 5 - 6^2 = 6.8 . a^2 + b^2 + 64 + 25 + 100 5 - 36 = 6.8 . a^2 + b^2 + 189 5 = 42.8 . a^2 + b^2 + 189 = 214 , which gives a^2 + b^2 = 25 . Since a + b = 7 , we have (a + b)^2 = a^2 + b^2 + 2ab = 49 . 25 + 2ab = 49 , so 2ab = 24 , which means ab = 12 . The quadratic equation with ro