Question

Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be `24/5` and `194/25` respectively. If the mean and variance of the first 4 observations are `7/2` and a respectively, then (4a + x₅) is equal to ______.

पर्याय

• 13

• 15

• 17

• 18

Answer 1

Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be `24/5` and `194/25` respectively. If the mean and variance of the first 4 observations are `7/2` and a respectively, then (4a + x₅) is equal to 15.

Explanation:

`barx` = `(sumx_i)/5` = `24/5`

⇒ `sumx_i` = 24

σ² = `(sumx_i^2)/5 - (24/5)^2`

⇒ `194/25`

⇒ `sumx_i^2` = 154

x₁ + x₂ + x₃ + x₄  = 14

⇒ x₅ = 10

σ² = `(x_1^2 + x_2^2 + x_3^2 + x_4^2)/4 - 49/4` = a

`x_1^2 + x_2^2 + x_3^2 + x_4^2` = 4a + 49

`x_5^2` = 154 – 4a – 49

⇒ 100 = 105 – 4a

⇒ 4a = 5

⇒ a = `5/4`

4a + x₅ = 5 + 10 = 15