Question

The mean of 5 observations is 4.8 and their variance is 4.56. If three observations are 2, 3, and 5, the other two observations are ______

Options

• 4 and 8

• 6 and 8

• 5 and 7

• 5 and 9

Answer 1

The mean of 5 observations is 4.8 and their variance is 4.56. If three observations are 2, 3, and 5, the other two observations are 6 and 8.

Explanation:

Let the two unknown items be x and y, then x = 4.8

⇒ `(2 + 3 + 5 + x + y)/5 = 4.8`

⇒ x + y = 14

Here, variance = 4.56

∴ `(2^2 + 3^2 + 5^2 + x^2 + y^2)/5 - ("mean")^2 = 4.56`

x² + y² = 100

Solving, x = 6, y = 8 or x = 8, y = 6