Question

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is ______.

Options

• 28

• 30

• 35

• 38

Answer 1

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is 38.

Explanation:

Let x₁, x₂, x₃, x₄ and x₅ be five numbers and one of the excluded number be x₅.

Given, mean of the five numbers = 30

⇒ `(x_1 + x_2 + x_3 + x_4 + x_5)/5 = 30`

⇒ x₁ + x₂ + x₃ + x₄ + x₅ = 150

⇒ x₁ + x₂ + x₃ + x₄ = 150 – x₅

On dividing both sides by 4, we get

`(x_1 + x_2 + x_3 + x_4)/4 = (150 - x_5)/4`  ...(i)

 Given, mean of the four numbers = 28

∴ `(150 - x_5)/4 = 28`  ...[From equation (i)]

⇒ 150 – x₅ = 112

⇒ x₅ = 150 – 112

⇒ x₅ = 38

Hence, the excluded number is 38.