The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?

Question

Question

This question was previously asked in

RRC Group D Previous Paper 17 (Held On: 27 Nov 2018 Shift 2)

Answer 1

Calculation:

Let the numbers be x_1,x₂, x₃, x₄.

The mean of four numbers x_1,x₂, x₃, x₄ = 37

The sum of four numbers x_1,x₂, x₃, x₄= 37 × 4 = 148.

The mean of the smallest three numbers x_1,x₂, x₃ = 34

The sum of the smallest three numbers x_1,x₂, x₃ = 34 × 3 = 102.

∴ The value of the largest number x₄= 148 – 102 = 46.

The Range (Difference between largest and smallest value) x₄ – x₁ = 15.

∴ Smallest number x₁ = 46 – 15 = 31.

Now,

The sum of x₂, x₃= Total sum – (sum of smallest and largest number).

⇒ 148 – (46 + 31)

⇒ 148 – 77

⇒ 71

Now,

The mean of the Largest three numbers x₂, x₃, x₄= (71 + 46)/3 = 117/3 = 39