Question

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

Options

• a = 3 and b = 4

• a = 0 and b = 7

• a = 5 and b = 2

• a = 1 and b = 6

Answer 1

a = 3 and b = 4

Explanation:

According to the question, 

6.80 = `((6 - a)^2 +  (6 - b)^2 + (6 - 5)^2 + (6 - 8)^2 + (6 - 10)^2)/5`

`\implies` 34 = (6 – a)² + (6 – b)² + 1 + 4 + 16

`\implies` (6 – a)² + (6 – b)² = 13 = 9 + 4

`\implies` (6 – a)² + (6 – b)² = 3² + 2²

∴ a = 3, b = 4