Question

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is ______.

Options

• 40

• 45

• 49

• 48

Answer 1

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is 48.

Explanation:

`(2 + 4 + 10 + 12 + 14 + x + y)/7` = 8

x + y = 14 ...(i)

`(2^2 + 4^2 + 10^2 + 12^2 + x^2 + y^2)/7 - 8^2` = 16

x² + y² = 560 – 460

x² + y² = 100  ...(ii)

⇒ (x + y)² = 14²

x² + y² + 2xy = 196

⇒ 2xy = 96,

⇒ xy = 48