Two years ago the mean age of 40 people was 11 years. Now a person left the group and the mean age is changed to 12 years. Find the age of the person who left the group.

no of members = 40

Mean age two years ago = 11

Let x₁, x₂, …, x₄₀ be ages of family members.

We know,

Arithmetic mean of x₁, x₂, x₃, …, x_n (n observations) is

Therefore, two years ago

⇒ mean age,

⇒ x₁ + x₂ + …+ x₄₀ = 440 [1]

In present, age of each family member will be increase by 2, therefore ages will be

x₁ + 2, x₂ + 2, …, x₄₀ + 2

But as a person left the group, let his present age be 'x' years

In this case, Sum of ages will be decrease by 'x' and No of persons will be 39.

⇒ Present mean age,

⇒ 468 = 440 + 80 - x [From 1]

⇒ x = 520 - 468

⇒ x = 52

Present age of that person is 52 years.